The goal in listening to your recording is to hear everything a little better than your target audience. Cheap speakers or headphones will hide some flaw that someone else (even with cheap speakers or headphones) will hear clearly.
Headphones: Headphones are difficult to use in mixing. If you do use headphones get some really good ones – expect to pay over $100: Sony V6, AKG K240 (I use AKG K141 which is less money). You have a choice between open back headphones and closed back headphones. Open back are often easier to build and make sound good, but closed back block out noise in a live sound environment. The AKG headphones are open back and will allow outside sounds to come in to the headphones. The Sony are closed back allowing you to listen to the track rather than the band.
Studio Monitors: Unfortunately most inexpensive studio monitors sound terrible.
Listen to some really nice studio monitors that are set up correctly. Take music that you know that is more than just “thump, thump, thump.” Specifically get male and female vocals and acoustic instruments. First listen to the monitors you can’t afford (one of my favorites is the JBL LSR 6328) and then pick the ones you can afford that sound as close to them as possible. If you can’t afford something that sounds decent – stick to headphones and save your money. You can always test out your mixes on your friends home stereo.
Monitor Placement: Most studio monitors are built to be operated without reflections. This means avoid room corners, walls behind the speakers but most importantly avoid reflective surfaces like desk tops or mixing console tops in front of the speakers. You do this by lifting the speakers above the desk and as close to the front edge as possible to still get proper aim. The interference (cancellation) caused by multi-path bouncing off a desk top is non-linear and no amount of EQ can fix it.
The center of the speaker should be at ear level or just below and they should be pointed directly at your head from a distance of about 3-5 feet.