Similar to weapons, Mods are introduced every other day. Unlike weapons, important mods are introduced first.
Engine - If you feel you are moving too slowly, definitely grab some Engine mods. Take note that Ocean stages slow you further, so you may wish to install more engine mods just for these stages.
Health - Quite possibly the most important mod to stack. The more health you have, the more leeway you have before dying! Also combines well with the Insurance skill, which lets you earn money from your health investment.
Reduce - If you're capped out on Health mods, considering maxing out Reduce mods. Anything that keeps you alive.
Shield - If you are particularly good at dodging, you may wish to get Shield mods instead of Health mods, or if you are trying for a heavy shield build. One interesting trick is to stack shields and use shield power-ups to restore your shields to full to maintain high health. If you're getting hit a lot (and you probably will), strongly consider investing in Health instead.
Regen - Similar to the above, you're probably better off investing in Shields. However, very high regen values can be achieved, resulting in powerful shields.
Accuracy - If you have mods left over, it may be worth putting some here. Useless for Chain, which never grazes anyway.
Evade - A pretty good defensive mod. Evade may let you completely negate a hit!
Crit - One of the few damage increase mods. Grab some if you have spares.
Item - Fairly useful to get all sorts of power-ups during combat. Worthless against bosses who do not spawn enemies.
Moola - It's risky, but if you are trying to farm cash, consider dumping a lot of mods into moola.
Exp - Similar to the above. If you are trying to farm levels, consider dumping a lot of mods into Exp.