If you've just moved house, it might not be the most urgent of your things to do. It is labour intensive rather than expensive (unless you insist on buying fine turf). If you are fairly strong but not used to digging and raking, then as well as aches and pains you may cause yourself injury by working too hard. Gardening injuries can be quite nasty and not too good to brag about. I have had tendon damage in my arms through over-enthusiastic gardening (not recently)
probably under the paving you will find lumps of concrete, bricks, diesel spills and hard subsoil. Also, once you have dug it over, it will benefit from being left for a few months to settle while you keep raking it flat.
Having done it a couple of times myself, I would suggest that after you have cleared and dug it, and given yourself at least 150mm of sifted, gritty soil (how you prepare it depends on what your existing soil is) level it as best you can, apply weedkiller, and a thick layer of organic mulch, and put pot plants on it. This will enable the humps and hollows to appear underneath, but it will look fairly tidy. Also any perennial weeds will display themselves so you can deal with them. When you are ready to seed, rake off the remaining mulch that has not rotted down and been taken into the ground by worms, and re-level the surface using sifted soil and coarse sand (unless you have sandy soil naturally) and treading it down.
If you feel the need to hire a cultivator, it will tend to make the ground settle very unevenly with ridges. You will have to rake and tread these flat several times over a few months as it re-settles.
It is useful if you have your own cat, as it will keep its own garden tidy and will fend off intruder cats.
You can certainly leave it the rest of the year, and start work again in spring.