Realistically, I would start by cleaning up what you have. This is actually a good time of year to move rocks and brick and anything else the PO dumped back there. I'd move the things like rocks and bricks to an area for stockpiling for now (perhaps behind the shed) and get rid of any trash or woody debris. You may well find uses for the rocks and brick such as creating steps or walls or non-flammable surfaces around a fire pit, so you don't want to get rid of them for now. If you don't have a heavy duty lawn tractor with a dump cart, get one to help you move things around the property and mowing. Learn to ID poison ivy regardless of time of year, with leaves and without. Start removing it by pulling it wearing protective clothing OR plan on spraying glysophate (generic Roundup without all the other herbicides) after it leafs out in spring and repeating every 4 weeks or so with any leaves that reappear. You can still get PI when there aren't leaves, so treat winter PI with the same caution needed for the growing season. Don't burn it - you can inhale the oil from smoke and end up hospitalized - but instead put in plastic bags for disposal. If you are particularly sensitive, you can get it from your pets' fur or handling clothing with urushiol (the rash-causing oil in PI), so keep your pets out of it and wash contaminated clothing multiple times in a separate load from other clothing. If you have deer, mice, voles, squirrels, etc. you will have ticks. You can reduce the number by getting rid of the brushy stuff under the trees, but you won't get rid of them, even with a gravel barrier, because the mammals cross the barrier, bringing ticks. Get in the habit of checking yourself, your dogs, and your kids for ticks every time you come inside (just a quick check) and every night a very careful check at bath or bed time including hair, armpits, ears, and groin. Talk to your vet about tick repellents for your dogs and spray your kids' clothing (not them) with a repellent containing DEET. I can pick up a tick between the house and the veggie garden which is all lawn, and during the spring can find 5-10 ticks a day, but haven't ever (15+ years in our current location) had one embed because I am extremely conscientious about tick checks if I have been outside at all. It takes more than 12 hours for ticks to embed, so if you are checking every night, it won't be an issue. Next spring mark wet areas, perhaps with stakes so you know exactly where you have standing water, where it stays damp for more than a few days, and where you have running water. IME trying to change drainage patterns without heavy equipment is usually unsuccessful (and potentially illegal in a natural wetland) but you may be able to slightly modify them so you don't have standing water and mosquitoes breeding. You can plan to plant long-damp areas with plants that are tolerant of moisture. This winter collect information and photos of rain gardens (particularly for shade), visit web and local resources that have information on wetland plants, and find a bunch of photos of dry creek beds and read up on how to create them so they look tolerably realistic. Based on many years as a teacher at a school with natural drainages through the school property, kids love playing with shallow running water- damming it, floating stick or leaf boats, etc., so don't put your drainage under ground. It usually is more successful anyhow to do a drainage swale or dry stream bed than trying to do buried pipes involves a lot more knowledge since underground the water needs a consistent slope and somewhere lower to go to, and pipes need sizing for your largest storms. Also, burying pipes in that area will be difficult due to roots, rocks, and the difficulty of getting a machine in there. Next year after you have drainage patterns established and have moved out rocks and debris, you can do some leveling, adding soil where needed to fill holes that aren't part of your drainage pattern. If you want to keep healthy trees, don't put much soil over large areas of tree roots, however. Then spend the next year IDing what you have (photos on the Name that Plant forum are a great idea) and deciding what you want to keep such as good climbing trees, plants with good fall color or nest sites or whatever, and finding someone with a good reputation for thinning woodlands and the proper insurance. Only after next growing season will you have enough information to really get to work on getting the area thinned out and starting to replant. You should know that despite the inspiration photo you posted of the neighbor's yard, you probably won't get that result. Most grass doesn't grow well in shade, and you said you wanted to keep more trees. Also you have water issues unlike what appears to be drier in the yard pictured. You may do better to have islands of plantings with mulch over the other areas, though you can try growing grass and then changing over if that doesn't work. Good luck - it looks like this project will keep you busy for quite a while!

At $500-600, you can choose from some nice Snappers, Toros, Hondas, Ariens, Lawnboys, and probably some others I'm not thinking of right now. Gasoline shouldn't be very messy with a decent fuel container. But as for noise, I would reiterate my recommendation to get an OHV engine. It's possible that a Honda or Kawasaki engine would be quieter than the Briggs and Stratton Intek and Dove (OHV) engines, although I'm not totally sure about that. Self-propelled mowers have transmissions that take power form the engine to move the mower, so you don't have to push the mower at all. IMO, it's a huge benefit if it works well. In this price range, the drive systems do work well. Electric start is a fancy add-on to some engines, whereas most are just started with a pull cord. IMO, this is not terribly useful unless you have physical limitations that make pulling the starter cord difficult. Otherwise, they add weight and complexity that is not needed. As for sharpening blades, if you have a grinder or Dremel tool you can sharpen them yourself easily enough. Otherwise, a dealer can do it while you wait if you take him the blade and should charge a very small amount. Which is a good segue to a very important point: dealership support. At this price point, you can stay away from the big-box stores and buy from a real mower dealer. This brings with it good after-sales support. But it also gives you the chance to find out much more before the purchase, so you can make the correct purchase the first time. At a dealer, you can put your hands on these mowers and hopefully even start one up and try it. You will learn first-hand what the various self-propel systems feel like, and how hard it is to pull-start the engines, and how loud the various engines are. For someone who is still learning the basics, this kind of service is invaluable. I can't stress this enough. I don't know about that Craftsman mower you mention. If it's been sitting a long time, it will likely be hard or impossible to start unless you clean out the carburetor. And it certainly won't be the quality of mower you will be able to buy in your price range. So I guess I'm saying that if you try to use it, don't let it form your opinion of what all gas mowers are like. There are true, real differences between budget mowers and good mowers. I'd venture to say that some people with aversions to mowing could be cured just by having good mowers! Good luck in your search. Feel free to keep posting questions here, and keep us posted.

MDob - I'm in a similar situation as yours in the 1.5 acres of lawn...but I only have 1 acre of "extra". My 1.5 acres of lawn is pretty much all grass (thanks to WeedBGone Max), but an unknown mixture of various grasses depending on where you are in the yard. The original owner who built our now 5 yr old house obviously went the cheapest route he could go to have 1.5 acres of "green". I also have my yearly battle with European Chafer beetles which is a costly battle. One question not asked here is what is your soil composition? Sandy? Clay? I ask because ours is so sandy that I can't keep the 1.5 acres properly watered...don't have a sprinkler system. There is NO WAY I could start my whole lawn from scratch and keep a newly seeded lawn from dying. Just too big. I guess what I'm saying is that "might" it be better if you WeedBeGone Max the lawn now, then slit seed it after the appropriate wait time? It's a chemical yes but you can't have your cake and eat it to can you? What do the experts here say? Between Mo Nature and me I think I could keep enough moisture on the seed to get it established before winter. Or maybe just do 3/4 acre now then 3/4 next fall. I'm confused and I hope I haven't confused you more!!!

It's hard for me to do the math in my mind and picture how thickly your trees and shrubs will be, but from my experience, it will be easiest to maintain if you put down newspapers, several sheets thick and then a few inches of mulch over that to keep the weeds down. If you call around, you might be able to find free mulch. I got a huge load delivered free to my house from a tree service company. It's not as nice as the stuff you buy but the price was right and I got it in the winter so it was free of leaves which makes it break down more slowly. Or your city may have a recycling facility with free or cheap mulch. I agree with Mosswitch. I'd put it right over the grass instead of trying to dig it all up. I'm not familiar with Maryland's climate but you may need to water them the first year or two when it's dry. I am quite jealous that you got all those for free! Wow! Sounds like you're going to have lots of berries/seeds for song birds. Spicebush is a host plant for Spicebush Swallowtail butterflies and Sweetbay Magnolia is a host plant for Tiger Swallowtails. Nice bonus.