i know what you mean there
i had an lp studio
ugh awful one

i have a epiphone special II somewhere. it's their lowest end les paul wannabe hehe. the LONGEST it ever stayed in tune was about 25 minutes. that is, until i replaced the tuning pegs.

only problem now is that i wasn't exactly sober when i performed the 'upgrade' and installed the new pegs backwards so you have to twist them 'wrong' BUT it stays in tune now heheh

hahaha
i tried a few upgrades
but ultimately the best was getting rid of it and buying a maton

yeah you get what you pay for with epiphone. they're good for a transition between a no-name starter guitar and something more significant though. they're also built like tanks (in my experience). i've thrown mine around a few times and it's still kicking. i have no plans on ditching it either even though i have a much nicer LP style guitar, it's a good backup beater.

pretty much my exact experience
my 2nd guitar
coming from a samick strat copy
threw it across a room violently more than once
dropped it down a flight of stairs
held up quite well
then sold it

i don't think i could get more than about $100 for it so i'd rather just keep it as a souvenir of my youth hehe. this way i can also pass it off to friends who want to try their hand at playing guitar but don't want to buy one just yet. which is why it's been in a friends closet for over a year now, i think his gf plays it more than him hehe.

i also have a niece who'll be hitting her rebellious teen years soon enough and i figure i can be the cool uncle who hooks her up with an electric guitar, which also provides great aural revenge against my sister hahahaha

Yeah i passed it off to a friend....who ended up giving $350 for it which was very nice.

Fender. Precision or Jazz. I'm sorry if its the standard response, but its standard for a reason. Go with a Jazz (or a copy thereof) for more versatility. Try Squier if you've got a real tight budget, a Mexican fender if you can spend a little more, or a Geddy Lee Jazz if you can extend your budget.