I've chosen "role player", though I'm quite a puzzle solver too (and of course i like the battles and stuff like the first option, but I don't think that's what leads the game). I like to give my characters names and surnames, sometimes making a party in which some or all the characters are related (brothers, sisters, parents, married, etc).I also give some of them mysterious names and backgrounds, like "The One" or stuff like that (usually not that obvious). Unfortunately, linear games don't give me such a good time in this aspect. That doesn't mean I don't enjoy them, I do, and a lot. But I think most of the (pc) games should give a little more importance to this matter - I'm yet to see a game in which you can play an evil party and have as mcuh possibilities and fun as if playing good ones.
I normally try to roleplay, but after trying that with TOEE (and developing a touch of multiple personality disorder) I found that I needed to apply a bit of min/maxing. I just about coped through the game, found the temple levels not too hard, but then when I met Hedrack I was lucky if my party lasted 3 rounds... There was nothing for it but to load an old save game (Dropping a load of levels, but not doing all the Homlet wandering again) and start actually maximising the abilities of the group.
For me, it's a combination of everything. If I want a pure puzzle game, I'll play Myst. If I want to larp in front of the PC, I'll wear a suit of armour. I never min/max. I like characters with flaws I guess. More seriously, I do think that puzzle solving is an essential part of any game. Intensive hand-holding is annoying but at the same time puzzles do need to have some logic to them - just so you get that 'doh - why didn't I think of that earlier?' moment upon completion. Actual roleplaying is quite difficult with a PC game. Essentially the modder is trying to act as the DM through his choice of options which he presents the player. But the modder's idea of roleplay is not always that of each individual player so for me increasing roleplay within ToEE involves more use of the dialogue options available in modding to increase both options and immersion (little things like an NPC noticing that he is talking to an elf has an impact which is far greater than you'd imagine if done fairly consistently - and do people like half-orcs or are they a bit racist about them...?). The actual min/maxing is a bugbear of mine. I don't powerbuild myself and modding to counter powerbuilds leads to overpowered encounters for those who don't powerbuild. I've no objection to tough encounters but sometimes, in some games, it can go too far. That said the open nature of ToEE leads to parties facing encounters which they can't win - but then that's life - don't go playing in strange temples if you don't think you can handle it Just my thoughts.