What's the best way to reach level 60 in ME1?

Speedrun the first on a lower difficulty and enjoy the second on a higher one. For one thing, you'll be starting off with some better gear and that alone will make the going less tedious... and you'll have a more complete character (potentially with the various NPCs from all the side-quests showing up or emailing you) to import into ME2 and ME3 playthrough). If you do the reverse (a speedrun after a complete playthrough), you would wind up importing the speedrun result... and lose out on hearing from some of the side-quest NPCs in ME2 and ME3).  If you feel that your XP just isn't high enough near the end of the first playthrough, you can always opt to do a few sidequests in that playthrough just before Ilos (the game doesn't stop you doing this) or opt to kill more things outside the mako in your second playthrough... but it really shouldn't be a problem.

Alright, thanks. I've already started my speedrun, hopefully it will work out. I might do a few easy sidequests along the way just to be sure. Hopefully I should be finished by tonight so I can enjoy the story better tomorrow.

If you do everything in your first playthrough, you can reach level 56 or 57. Speedrun the second playthrough will get you to level 60. I've done that a couple of times

Let me put it this way... If this was your first ever playthrough of Mass Effect with your gamer profile (on the Xbox at least), you would be capped at Level 50 (after that you simply don't earn any more XP).  I've done a few playthroughs with new profiles to test this, and I generally hit this Level 50 cap on a completionist playthrough near the beginning of the Virmire mission... long before I reach Ilos.

After you beat the game once, you earn XP at a faster rate and you are no longer capped at Level 50... making it possible to reach Level 57 in one completionist playthrough and with not killing any enemies inside the mako.  You will still required a second playthrough to go from Level 57 to Level 60; but you will generally hit that Level 60 long before you reach the end of the game (if that second playthrough is also a completionist one).

If you do a quasi speedrun first, basically just doing the main missions and maybe BDtS and a few of side mission planets and kill everything outside the makeo, you will probably still get into the 40s on that first playthrough.  If you then do a completionist playthrough with your second one... again, refraining from killing enemies with the mako, you will be able to get to Level 60 by the very end of the game at Ilos... and you'll be importing the completionist playthrough rather than one that has a bunch of side missions missing from it.

If you want the file you import to be the complete one, then it only makes sense to do the "speed run" first.  If not, then by all means, do the completionist playthrough first and the smaller one second.