Different people my give different advice, which is normal. You are the
final judge and decision maker.
My recommendation would be this:
1. Do it yourself.
2. Renovate both the front and back yards in the fall, not now.
3. Do a soil test.
4. Do soil drainage and compaction tests.
5. Amend the soil from soil test results between now and the fall. It might
be laughable to do so before planting in the fall, but eventually you'll
realize that you have the final laugh.
6. [Optional] If you like to gain some experience or do something for fun,
just buy some crappy seeds from the big box stores, throw them down
somewhere you like in the spring while adding some starter fertilizer, water
them and see how they grow and compete with the weeds, with the thought
that all of them will be killed in the fall for new planting. No tillering,
no aeration whatever. You can also buy chemicals to kill weeds during this
time to gain some weeds handling experience.
7. Learn more about grass and renovation before fall. Especially decide
what grass you'd like to grow and buy quality seeds (not from the big box
stores).
8. When fall comes, you'll be in a pretty good position for a renovation.
8.1 Round up the yards for about 3 weeks. Since you have time, you can
probably do 4 weeks. 2 weeks is the minimal. Be careful not to spay on the
nearby trees.
8.2 I strongly recommend against tillering (i.e. not disturbing the soil),
and would also recommend against aeration unless absolutely necessary (e.g.
you are pretty sure that your soil is very compact). If you heed this
advice, not only will you save money, time, and laboring, but also you'll
have much less weed pressure later. Does it work by throwing down seeds
directly on the soil without tillering? Yes, it absolutely does.
8.3 Spread seeds and starter fertilizer and a thin layer of top soil or
compost or peat moss and water lightly a couple of times daily.
9. The next spring you'll need to put down a pre-emergent since you have
crabgrass history. Roundup and no-tillering won't do away with the
crabgrass seeds already in the soil.
There are more details to step 8, but by the time it comes, you'll probably
already know what those are.