The control scheme demands precision, so you should spend some time just learning the ropes -- jumping around, flipping, leaping to grab stuff, when you need to hit the jump button during a sprint to avoid running off a ledge, etc. Once you intuitively can get the controls down, the exploration gets ten times more fun. And there'll be plenty of that, since the levels are fairly massive and have many secrets to uncover. [The game can be a bit glitchy, for better or worse, though.]
Oh, and Lara's default pistols don't use ammo, so they're a good standard weapon for most encounters. You'll want to save shotty and magnum ammo for the more annoying foes -- don't squander 'em! Same goes for save crystals. They're found at set locations and are one-time-only, so you'll have to pick the best time to use the suckers. [Health, ammo, etc. doesn't get replenished post-save, so saving when in optimum condition can be a good idea.]
As a fun aside, if you're playing on the original CD, you can put it in a CD player and hear some clips and tunes from the game. Been awhile since I tried (in fact, I just threw out my player the other day!) but I think there's about 50 tracks when heard this way.
Take me down from the ridge where the summer ends And watch the city spread out just like a jet's flame