for my 2˘ based on very little experience except
extensive looking at boats to buy, the decision you need to make first is whether you want to go
sailing or
boat building!
I looked at 'cheap' to 'free' boats that needed major work to go sailing, and at somewhat more expensive boats that needed little beyond new exposed woodwork and a really good cleaning. I chose to go sailing
The other thing to consider is that operating costs increase pretty steeply with length. You can trailer a 19 ft or 20 ft boat behind pretty much most smallish cars. But get an extra foot or two and you need a truck. Much bigger than that and you need a slip, with annual launching and haul-out fees.
I re-read that you want a live-aboard, so you've pretty much bought into the operating costs already. So back to the first thought:
when do you want to move aboard? The more work you have to do, the longer it will take. I think a boat is too small to live on and do major work, though anything is possible if you put your mind to it.
I second
Faster - buy the best condition boat that meets your needs (you fall in love with it

) and is within your budget. Allow twice the time and twice the money for any improvements! And go sailing, unless you really,
really want to become a boat builder....