I inherited something similar when we moved. I also seem to spend more time with my workmates than with the much beloved. however, I know it seems like a daunting task but it can be done, I'd say we're at 25% of where I'd like to be but I have to keep pinching myself and reminding myself that it's not going to happen overnight, although the weeds do seem to happen overnight!
The best thing I personally can advise is section it off, ours seems to naturally fall into 4 sections, front, back left and right! The house and hedges are covered in Ivy which might appeal to some people but it's taken over everything. The people before us just cut the grass and that was it, we've bushes and hedges running ferral!
So the 1st weekend we could we hacked back (and I mean right back to stumps) the bushes to the right and back of the house. We also took out the lower branches of a lydani (spelling?) which is bigger than the house. We didnt go any further than I could reach because it soon became obvious we had LOADS of bird nesting. We've decided to wait until after summer before we take out the trees we want to, to let in the light to let the chicks do their thing.
We also took a chunk out of the bases of the Ivies in the hope of slowing them down.... which it seems to have done.
What this has done has opened up the garden, it would seem we have 6ft boarders we didn't know where there... I kid you not! I've not done anything with them yet.
Once we can take out the big trees, there are 5 possibly 6 to come out and got the Ivies and Laurel under control a bit we can start on the boarders etc.
It's going to be a long haul but we aren't planning on moving for a long old time, if ever!
So I suggest the best and cheapest way would be to find a willing nephew or other child labour... sorry, willing volenteer who will help you out and let them loose with a strimmer to get the lawn under control.
After that you can maybe organise a bbq with friends and family where the all take a section and clear out their bit you can feed them for payment, we used to do it at my Grans, it was great to get everyone together for reasons other than wedding funeral or christening.
Once all the rubbish has gone you can see what you've got left. don't worry about hacking something thats a plant, if it's worthy of your garden it will come back again when it get some light through!
I also suggest once your clear you take some time to decide what you do want and where you want it. We had a poop corner for the Pooches at Grans so when any of us had our dogs with us they all went in the corner to leave any little parcels, easier to clear up and we didn't have to worry about the kids playing on the grass.
But the main thing is just remember you cant do it over night and if you take a section at a time you get there before you know it, maybe clear your reading area 1st so you can have at least one bit you can use?
Wow you can tell the footies on... I'll stop rambling now!