To be honest you appear to be between a rock and a hard place. You either try and turn the 'grass' back into a lawn or you kill it all, put down membrane and then a big load of chips.
The first is a lot of work and the second is a lot of money!
If you want to try and turn it back into a lawn, strim the worst of it and then try to borrow a hover mower which will cope better with the unevenness of the ground. Once it is all cut down, you will then have a better idea of what you have. You may have to get a load of topsoil to even out the low bits and reseed. Keep it watered and nurtured. You may be lucky and once it is cut, it may not be as bad as you think. In which case reseed the bare bits and give it all a good dose of weed and feed. Keep it on a fairly high cut for the rest of the year to recover.
Using Pathclear two or three times a year will keep the patio area weed free all year. I normally give it a spray in April once the weeds start growing then follow up in July and sometimes in September. Pathclear will kill the soil as well so there should not be too much regrowth if you keep on top of it.