You have to leave some space between plants anyway, so what I generally do is place some inexpensive pavers here and there to walk on--they also make an impermeable "mulch" around veggies that don't cast much shade. Right now it's probably still cool enough for you to be planting peas, radishes, lettuce, spinach, and cabbages/brussels sprouts/broccoli/cauliflower, none of which enjoy hot weather. The peas and radishes will be gone first, and eventually the spinach and lettuce will also give up to the summer heat, so do your spacing with that in mind. Swiss chard and beets can also be planted now, but will last longer...chard will take some frost so is a good veggie to plant if you like it. Onion starts and green onions (from little bulbs) can also be planted early. For your space allotment, you would be better with peas (and later, green beans, if not tomatoes) as climbers on tripods or netting on the side of your bed away from the sun so they don't shade other things. You could plant your tomatoes (or green beans) where the peas were, as they should not be planted until comfortably after your last frost date, but a few weeks later will still get you tomatoes. You could plant zucchini where the lettuce and radishes were. Etc. If you plant peppers, which generally have a similar growth habit to tomatoes, but a bit smaller, plant then about the same time as tomatoes--when it is consistently warm with no possibility of a frost. Plan to plant any vining crops like cucumbers, winter squash, zucchini, etc. on the edge of your bed which faces the sun the longest. The sun will draw them away from the bed so that they won't compete as much with whatever else you have planted. They are the most susceptible to cold, and are usually planted some time after tomatoes and peppers. Bush zucchini can also get quite large and cast a lot of shade. Someone else will have to advise you about carrots, celery, potatoes...I am not experienced with those. If you like artichokes, though, you should try them. You will have faster results if you purchase pregrown cabage family, tomatoes, and artichokes, but it's a waste to spend money for starts of lettuce, spinach, and most other vegetables...most of the vine ones do fine direct seeded asa the weather is consistently warm, which is when tomatoes also do best...but it does stretch the growing season to use plants for those with the longest times to maturity. Tomatoes will survive before the weather is consistently warm as long as there are no frosts, but not do as well as if you had waited. Ones planted at the optimal time will usually get just as large as those planted earlier, and be more productive. If you plant full sized tomato plants, tomato cages are advisable, and they would also be helpful to pepper plants and Brussels sprouts. Obviously, you will not be able to plant all of these, but will have to choose which you like the best and go from there. Tomatoes are usually a priority for most, and three or four well grown plants properly spaced can yield a good quantity of tomatoes. If you like hot peppers, the Thai ones make a small plant and produce quite a few little red peppers toward the end of the summer. Brussels sprouts take up quite a bit of room, but can be picked over a period of time, unlike cabbage. Some varieties of broccoli are especially good at producing side shoots when the main head has been cut off. You can get quite a few green onions with one short row, if you like them. Peas and green beans, if kept picked when ready, will keep producing (peas only until it gets hot). Ditto with zucchini and cucumbers. The winter squashes are usually not ready until late summer, but if you pick some green for summer use it will sometimes stimlate more to be developed. The vegetables that don't do well in heat either die (peas) or start producing seed (lettuce, spinach, broccoli, etc.) In some countries, radish seed pods are pickled, I have noticed. Also, I think radish leaves make a tasty vegetable, either steamed or stir fried. So do beet greens.

I have a huge perennial garden (no shrubs) on a septic mound in my backyard. I knew I couldn't afford to put bark mulch down in such a large area and didn't want to deal with vinca (have it elsewhere though) or landscape cloth, which is such a nuisance when you want to add something. So I put in a few pots of a very shallow-rooted sedum that blooms in the spring. It is now everywhere, so I have to fight to keep it out of the lawn, but it does a pretty good job of holding in the moisture. I know it also helps keep down the weeds because wherever I remove it, I soon get a crop of weeds and/or grass.

Liriope spicata and euonymus fortunei (wintercreeper) are both fast-spreading and good in full sun on slopes. They can each be invasive but not as bad as ivy.

I agree with Annie; setting realistic goals is important. Your budget is also a consideration, and how much you like to garden. What do you want the front of your house to look like? Do you envision a flower garden, a grassy slope,or a nicely landscaped area with a mix of shrubs and plants? My approach would be to Roundup the whole slope, after everything dies, pull out everything, then at least you'd have a 'clean' look. Then in the fall, as Loretta mentioned, do your planting. I think at this time of year, you're fighting a losing battle. Looking at your picture, it doesn't look like you have any edging material there, so I'd add some, till, add a fresh layer of topsoil, and start planting whether it's seed, sod, ground cover, or mixture of plants. Water regularly and the new plants will take hold, overwinter, and by spring those weeds won't have a chance. IMHO-If you choose the groundcover, stick to one type. I'd have a lot of fun landscaping your hill by adding some base plantings of a small tree or two, evergreen shrubs, rhodedendrons, azaleas hydrangeas, or some other plants then a stretch of perennials, and on the lowest part of the slope add ground cover. Mulch around everything. You'll have minimal weeding to do, a lovely look, and no mowing. I did something similar in stages over time(my kids were younger at the time)except I have grass at the lowest part, but if you go this route, it's important to put your ideas on paper first. J