The more pertinent question is the state of your rough grade compared to what the desired final grade needs/wants to be. If it entails bringing in topsoil to raise the final grade, or leveling to slope away from the house for proper drainage, you'll want to do the necessary changes within the intended planter areas before you plant. On the other hand, if drainage is already okay as is, and any plantings you do now are only temporary or can be easily moved; there may be no need to wait. Were you also intending to put down a temporary walk as well? If so, crushed rock or gravel over weed fabric,perhaps with precast concrete pavers 2 foot square might do decent temporary duty at little expense. To get more specific advice based on your actual conditions, you could also contact a landscape contractor or designer and have them consult for a couple of hours and give you more accurate site specific advice. Sorry to hear your move-in hasn't started off smoothly, good luckily with getting a temporary start on a new garden going. You might even consider seeding some green manure type plants in the beds to increase soil fertility and humus content that could be rototilled under in the fall, along with local wildflowers. Alfalfa or clover seeded over future lawn area and plowed under later would also be beneficial to build up the soil.

For reference my directions are as viewed from the street looking at your house. The first pic, that's neighbor on L? The scar on R of fence is where your shed used to be? R half of 2nd pic is neighbor straight back...L half pic your yard (aiming toward neighbor with shed)? The third pic I know what is but I cannot differentiate levels. Sorry. Looks like that lot high, too? The neighbor directly straight back (w/2 large trees) looks like he's been high forever as if subd. created that way. The neighbor on you L side looks like his fill might be much newer. His grass has a new-ish look. (would have liked to seen a pic aiming further left...I'm trying to see where the drain path goes.) Aside from the water, he's dumping on you, where's the rest of his water draining? To his front? And the guy next to him (past power pole) where's his water going (other than what he's putting on you)? If the bulk of their water is going to the front...which you might be able to tell from standing in front of their houses, I'd guess one or both of them has blocked your natural flow. Which says that going to a lawyer for a consultation to discover your rights and make a plan is the place to start. Someone pointed out, what will you do with major rain like hurricane Irene type rain...or the hundred year flood? Your original plan will put you in jeopardy if such were to happen. Actually, with your drainage blocked, you're probably already in jeopardy. just won't be able to see it until that monster rain happens. I'm not trying to be an alarmist, but I think it's important to know where you stand legally...especially, if you can get the cause of your problems to pay for the solution. I would try to find out every last fact about where that water is draining...how it's draining for these neighbors...get out their during the next heavy rain. Take pictures. Make yourself knowledgeable about exactly how all these pieces of the the puzzle fit together...before going to lawyer. You don't want to go with just a few words and a complaint...to which he says, "we'll need to study your issues. That'll be $500 for our next hours worth of work." Go as prepared as you can be.

55 years ago I mowed my neighbors yard. In front of his house he had two mature Catalpa trees. Those two trees are still there and are still very attractive in the front yard. There were no roots coming to the surface and it was very easy to mow around. I think the Catalpa tree is one of the most under rated tree for use in the landscape. Not only does it have a very attractive shape, in the spring it is very pretty when it is in bloom. The flowers are shaped like orchids, and have a very sweet pleasant aroma. SO in my opinion the positive well out weigh the large beans that form. (They are easily mulched up with the mower.) You can see these at least 80 year old trees on Google Street View at 817 South Webster Road New Haven Indiana.

Pragense viburnum, easy, but will need to be trimmed regularly. Very hardy. Deer resistant. Euonymus japonicus, maybe 'Aureo-marginatus' (Golden) or 'Chollipo', 'Silver Queen', others. In the south they can get scale. I've never had a problem in 12+ years. Deer love them. Euonymus kiautschovicus 'Manhattan' , a bit course, but very fast. Needs shaping. Deer will munch on them, if they are a factor. Osmanthus heterophyllus - spiney, tough. Slow growing. Deer resistant. Osmanthus x fortunei -- can get eventually to 15 feet. Will need shaping. Spiny, deer-resistant. Fragrance in fall. Hollies - there are so many. Certainly one to fit your space. Some are spiny. Look to Japanese hollies such as Steeds upright, Convexa, or hybrids like 'Spartan', 'Castle Spire', 'Fosters', 'Blue Maid', 'Centennial Girl', 'Liberty', etc. etc. Usually deer resistant, but you never know. Dwarf Burford holly. May get some late frost burn, but otherwise very tough. Spiny, glossy leaves. Will grow more slowly though. Easy to shape. Regular Burford grows faster/taller/wider, but needs more shaping more regularly. Prunus laurocerasus 'Schipkaensis'. very hardy, but needs extra water in droughty times. Other than that, it's pretty easy. Upright evergreen leaves. Should be good for cooler zone 7. Deer resistant.