Used are a complete lottery ... you could get lucky but it's best to assume you're buying a candidate for rebuild - it's rare these days to come across a running engine in the car that's driveable - and true low mileage engines as rare as rocking horse sh*t - the last A series fitted to minis were 2001 so very conservatively assuming 5k annual miles from new then we're talking engine with 80k on....at worse one hell of a lot more
So to with an engine outt to maximise your chances of getting a good one - go for one with recent rebuild - you'd want to see receipts and take the head off for a cursory check- bore wear can be easily ascertained with a fingernail.and pistons normally carry a descriptive code on the crown.....knowing who build it is also always good....not every rebuild is properly done - buyer very much beware
Avoid what I term "ebay paint specials" like the plague - plenty of these about- i.e chunk of scrap generally full of rust and worn out with all the filth covered with fresh engine lacquer.- it's exceptionally difficult to return an a series to pristine in one piece - if you go to that much effort it's almost as easy to strip down and rebuild .....
Occasionally gems do crop up - i've a legitimate 17K MG metro lump & box, fully documented in perfect working order stashed (not for sale - sorry!) - history on the donor car is good and if a recent breaker a check of last mileage on MOT history goes some way....
A minefield ..... factor in a rebuild cost for both lump and box add to purchase price and that's your actual cost.... makes some from reputable suppliers seem decidedly less expensive!
Before I come across as too pessimistic one final point - check the engine number against guessworks number explainer.... to make sure (if in original state) that you're looking at something - particularly from perspective of compression and diff ratio, that would suit your requirements......