i definatly have to recommend you play it with at least 1 other person...it will get boring quicker if you play alone...however, with a couple of friends...you probably will have just as much fun while workin on playthrough 2(should you decide to)
i made the mistake of playin solo on 1 and 2, and i am gettin bored on playthrough 2, i get killed a lot cuz no team support and i am not finding good enough gear to resist the rediculously tough enemies

For the Secret Armory, find a decent weapon with x3 or 4 Fire and Corrosive dmg, cuz your gonna need 'em.
if your playing through, do all the of the missions. More XP then killing all the people, so you lvl faster.. and they're pretty easy, especially when you know where the stuff is.

If your playing as a Siren, get a Hellfire and Phoenix skill to wtfpwn every Lance you see. If your playing as a Hunter, get the Trespass skill to one shot those aliens.

And check Borderlands Wiki for the red chest locations for each map. They usually give you the best weapons at or above your level.