I might seek another opinion. The type of mulch you use has nothing to do with foundation issues. From what little I know about such things after having a 'problem basement' years ago in OH, wrapping the basement walls is usually done all the way around the house. I don't see how doing one wall could solve the problem. Where does the water go from that drainpipe? It should go away from the house, not into the ground next to it. That looks like the problem to me from what little one can see in these pics. Does the ground slope down toward the house there also? The ground should slope away from the house. Then water flows away from it and doesn't pool up around the outside of the basement walls. There is no reason I would ever use rock as mulch. It's too hard to pull weeds out. I don't feel like I can see enough of what's to the left in the first pic to suggest any particular plants. Also have no idea where you are, what garden zone? Which way does this house face?

Okay first, you'll need to pull back those stones. If you don't have a 'hard rake' yet, invest in a good one. If you have one, and it's cheap, work with it until it breaks. If you need one, you will forever appreciate a good tool - get the best one you can afford. For a hard rake, you'll want one with 2 connecting points on the edges of the head (bow rake.) The type where the handle makes a single connection with the rake head is not designed for heavy materials, nor as good for long-term landscaping tasks such as moving stones or leveling beds (the back of a bow rake is perfect for moving a lot of dirt and putting a nice finishing touch on the project.) Get one that is size-appropriate for your height. These choices are what will take much of the drudgery and frustration out of already difficult jobs. Next, since it will be an ongoing project, break it down into stages. I do suggest that when it comes time to buy the plants, you buy all of the same varieties of plants at the same time. They can be like kitchen tiles. If you don't get the same exact shrub, at the same time, colors of both foliage and flowers may not match. Do all of one type at one stage, then later get all the next type, etc... If you have a decent size back yard, and can afford it, buy at least one extra of each shrub and plant it in an out of the way place, or in a spot where it can be moved later. It's not uncommon for a shrub to die, and a small investment ahead of time can save you headaches later if you need to fill something in. If you have so many plantings that this is financially a problem, skip it. Start with the rocks. Get a good size tarp, a wheelbarrow, and a round shovel. Start with pulling back the stones in the areas that will get the same plantings. Place the tarp on an out-of-the-way corner of the lawn and start dumping stones on half the tarp. Use the other half to fold back over to keep them clean and to keep the neighbors happy. This will kill the grass, so if you have extra driveway space, just dump them on the driveway and cover with the tarp. Keep removing more stones as you gather OM (see next paragraph.) Next step is to decide if you are going to buy the soil amendments, or build the soil yourself. Since you expressed a desire to build your own (the vastly cheaper route) begin piling on any organic matter you can. Either start a compost pile, or just start tossing on what OM you can gather on the now stone-free areas of the beds... or both. Some very cheap examples of OM resources are coffee houses (free,) wood chips from the companies that trim trees from power lines (free, or a small tip that makes them both happy to dump it where you need it, and happy to return with more,) kitchen scraps, grass clippings (learn how to compost these properly... a great source of organic matter, but a pain if not used correctly,) city leaf collections (even out of season, some cities use the same place each year and uncollected leaves piled up become what is called leaf mold... great stuff for lightening clay!,) and county dumps (many dumps in Tn. are now separating out all tree products and shredding them. They either give it away free, or sell it at reasonable prices to county residents.) There are many other sources for organic matter, just keep your eyes open and you might be surprised at what becomes available. Let it pile up high, and keep it pulled back a little (or really, just don't let it pile up too high) against any plant you want to keep. As it begins to break down (kept relatively moist, organic matter breaks down fast in Tn. My 8' of long grass and hay mulch on my garden beds broke down to an inch over the summer and was incorporated into the soil by the worms) add more and/or turn it into the soil (next paragraph.) Next you'll want to buy or borrow a 'garden fork'. You can use a shovel, but a good fork works better. At least once a year, and as often as every 1 - 3 months, turn the organic matter into the soil. If roots are in the way, you can keep it on top, or pull out the plantings that you don't want, and just mulch around what you want to keep. The worms will incorporate the organic matter into the clay around established plants, but it's a much slower process. If you did a good job at scrounging OM, you will be ready in a year or 2 for your new plantings. Of course, the longer you wait, the better, but strike a balance. When you dig clay, and turn in OM, the expansion of the volume can be surprising. Clay packs very tightly, once you begin to loosen it, you may quickly find you'll need to pull some out. This will depend on your desired level of the bed. When it comes time to remove the old plants, think about reusing them somewhere else, or use them as trade to get people to help. Lastly, decide what you do want as mulch. Organic mulches will continue to improve the soil and have many benefits. The downside is continual replenishment. Stones are fine, and when used with a weed barrier of some sort, look good and clean. The downsides are weeds that poke through when no weed barrier is used, the soil stays in a 'stasis', well-intentioned landscapers trying to weed eat around, or on top of stones inevitably break a window, and stones don't always stay in place... matching them, and replacing them ain't cheap. Anyway, that should get you started, and if you piddle around a little here and there, you'll be surprised at how fast removing the stones goes. BTW... a bbq gets family and friends more in the mood to help, and if you tackle the entire project in stages, the work for each step is nothing.

Thanks for all of the comments. I didn't expect to see so many saying no to the rock which is good information. The challenge and some have brought up solutions. I live on the prairie. very few trees and wide open spaces so the wind goes and goes just like the view. We have started to put up plants to try and combat the wind but things don't grow real fast and is challenging to boot with our winters. they are very unforgiving. Until the plants get large enough to help in the wind mitigation, what other options are there to keep the wood chips from blowing? that is where we were trying to figure out, could one do a mix of rock and the wood chips but it seems that might look goofy. This would be my wife and my preference. I will see if i can attach an image what the winter/spring did to what we had for reference. we have tried cleaning up as much as we can from behind me and in the grass. It was out a good 30 feet in to the grass. Maybe this is not uncommon but sure a pain. Gives you some idea as to why we were considering rock.

Personally I would plant mint. Lots of it, in all possible flavours. I understand you don't want to care for that corner much, in which case you need something that looks good all the time, not just two months a year. You can have a mix of winter cyclamen and hellebores, spring lilly of the valley (I have small kids and they are smart enough not to touch anything I tell them is poisonous), summer moss, autumn cyclamens (different than winter ones). However all this requires some maintenance, much more than mint :D Why not place a few aromatics? Like celery, parsley and a few pots of mint? ;) Also spinach, peas and lettuce would love to grow there. Or you could go for a trellis on the wall and let vinca grow on it, one with gorgeous leaves. I have a full north little space and the previous owners had the vinca and trellis. It looked nice but I preffered to reduce it in size and plant small pansies and many types of hellebores. It makes for a gorgeous front autumn and winter garden, less gorgeous in spring and summer.