Regular computer speakers are some of the most distorted sound sources you will ever hear, other than phones. I would recommend not tweaking a single setting on crappy computer speakers. Yes, you want them to sound good on everything, but that doesn't mean switch to computer speakers and start tweaking the bass. It means just check it on speakers every once in a while. Most people these days want to hear music on better systems. They won't go out of their way to criticize a song they're hearing on their cellphone. I am assuming you have bad computer speakers, because most are. But even if they have decent bass, they are not designed to be accurate.
A lot of monitors are good, really. There's a lot of debate about which ones to get, but in the end, you want an accurate mid-range, and most of them have that. I have Yamaha HS7's. They don't extend as far down in bass as I'd like, but they get the job done.
You will also get a lot of problems in untreated rooms. That's a whole can of worms we don't need to get into right now.
I'd recommend mixing in headphones at low volumes. I don't have a lot of experience with headphones though, so I couldn't tell you what the best pair is. I've had two pairs: The 100$ Sennheiser 280 HD Pro's, and the $300 (or so) AKG K702's. The AKG's were infinitely better than the Sennheiser's. They have a really wide stereo field and they have so much more clarity.
You just need to be able to trust what you're hearing. I remember when I was starting out, I watched a video on mixing, and this guy said he mixed on Apple Earbuds because if it sounds good in those, it'll sound great everywhere else, which is complete horseshit. You can easily make the worst mix of your life and have it sound great on earbuds. It could sound like a mess in the car. You don't want to mix on untrustworthy systems.
