I never had a problem with the stock tyres personally, in the wet I take it easy anyway, I only came off once, and that was down to me applying too much revs on a wet drain cover on a bend. I've replaced the tyres with Conti's now, but only really because I couldn't get a set of the michelins in time for when I needed them.
I personally wouldn't worry too much about the tyres, if you're buying second hand, just take the bike as it comes, wear the tyres down, and if you find them alright replace them for similar tyres or move onto different ones.
Never really had any major issues, just small problems. Had water/condensation leak into the clock, took it apart dried it, and sealed it with silicone when I put it back together. Had one of the chain adjustment bolts sieze on me, so had to remove the wheel etc. to get it out. The wing mirrors occasionally lose their stiffness so fold back when going forwards, take one bolt out, and clean or replace the washer there and retighten and they're fine for some time afterwards.
All round it's been a pretty solid reliable cheap to run bike, it's a decent size bike so you don't look like you're on a toddlers bike which is why I chose not to get a last generation CBR-125, gets you ready for when you move on to bigger bikes, it's not to dissimilar in size to the current R6. Pretty economical as most 125 four strokes are, looks pretty good, and looks a better quality than other 125's.
