Greetings,
Glad to hear that you are moving away from mowing. You are doing the right thing by getting rid of invasive plants first. If this were my project, I would do it this way.
1. Establish the area that is being planted. Flag any good natives that you do not wish to kill.
2. Spray everything with glyphosate (Round-Up). I know people are against herbicides sometimes, but consider that this could potentially be the last time that the area will ever need to be sprayed. Ever. Plus, applying herbicide to an area a couple times is a lot better for the environment than using gas to mow it every week.
3. If you start spraying now, you should get a good kill by fall. I would spray a couple times at least to get a good kill. Make sure all the tough bad guys really are dead. Hand pulling weeds work, but is way too labor intensive unless you have a lot of free time. Save your energy for weed control the first year after planting.
4. At the end of Fall, work up the soil lightly. Not a deep till as it will only stir up weed seeds. if you can work it about 2-3 inches it would be more than enough. Some areas may not till easily. Just rough up the soil if you can't till it.
5. As winter sets in, you will want to plant your seeds. Mix the seeds with a sawdust or tree shavings (sold at farm supply stores. Hamster bedding or sand also works). Spread it evenly over the planting area. The sawdust acts as an aid to help show you what is planted and to promote even coverage.
6. The winter snow and freezing-thawing periods will work the seed into the ground. They will come up without fail in Spring. Trust me, I have done this with a number of areas on my property and it works very well with everything except some of the grasses. For more info on this google "Frost Seeding Prairie"
7. In the first year you will have a lot of weeds come up with your seeds. Do not panic. This is natural. Keep the meadow to about 6" Most of the flowers will not get taller than that the first year. The best time to cut weeds back is when they are blooming. You can also pull them out if you have time. Do this until Fall. The second year you should not have to do anything except spot treat weedy areas by trimming, pulling, or reseeding.

Meadows require mowing once a year once established. This is done in early Spring before they start growing. Mow it to the ground (as low as possible). If possible, remove all clippings with a bagger or a rake. Removing the clippings allows the sun to heat the soil and thus heat it quicker. This in turns promotes meadow plants over invasive cool season plants. It also usually results in a better looking meadow. Some people suggest leaving some of lain last years growth up for nesting material for birds, but the choice is up to you.

As for seed...why not collect your own? Fall is a great time of year to collect seed. I usually collect as much as I can on my own and then buy whatever else I want to plant. Seed companies usually charge quite a bit for meadow seed, but if you want to go on the cheap, figure out a list of low-growing plants that you like and then just buy those in bulk. I don't like to spend a lot of seed, so here is a short list of awesome plants that do not cost very much and are easy to get established.

Black Eyed Susan
Yellow Coneflower
Purple Coneflower
Lanceleaf Coreopsis
False Sunflower
Little Bluestem
Indiangrass (taller, more aggressive, but very pretty. don't plant too much)
Brown Eyed Susan
Smooth Penstemon
Butterflyweed
Cupplant (best flower for birds)

I think I would wait a full year before planting seed. That way you could treat the area with herbicide multiple times over several seasons. The best time to treat is when plants are actively growing in fall and spring. Fall is the best time to apply herbicide with spring being the next best season. The other advantage of waiting a full year is that the dead sod will have decompose appreciably allowing for better seed-soil contact. In that year, you will be able to educate yourself and possibly join a native plants group, like Wild Ones, where you might have access to some free seed. I Like the idea of a short grass prairie for beginners. The grasses would be limited to prairie dropseed, side-oats grama, and little bluestem. Short grasses show off flowers better. You can always introduce taller grasses later.

While not native, deer, bees, and butterflies love clover. I would plant crimson and white clover over most of the area. Make sure it has been inoculated. Clover will add quite a bit of nitrogen to the soil. It looks great too.

I like Nick's plan for getting started.

If the soil is acidic enough (soil test will tell you), I would put several blueberry bushes, native azaleas, dogwoods, and serviceberry trees around the perimeter. Some crabapples would look good too and critters like them too. Persimmons are good for raccons.

For spreading seed, you can use a push style seed spreader from the hardware store. Get the best one you can afford. The seeds can be had at any good seed seller, co-ops, and maybe even from your state or county.