Just went thru all of this with my company plan, so I'll add $0.02.
HSAs are a nice option for some people. The basic concept is that they are tied to a high deductible ($1000 or more) insurance plan. You can then "save" up to your deductible amount in an IRA type of account. As far as paying for ordinary doctor visits, if you go to a doctor in your plan you should get the plan rate if you have the doctor submit the bill thru your insurer. They apply your deductible and you pay the plan rate. Obviously, you may want to check this over closely. There is one drawback, you cannot have prescription drug coverage (ie; $15, $30, $50 drug card). Drugs are paid out of your HSA and then picked up by the insurance after you reach your limits. Bottom line, if you are young, don't need drugs, and never see the doctor it is probably a good deal. If you use the system and have a regular prescription, then the old way may be better. You have to do the numbers. Frankly, when I looked at the premium rates for my company I didn't feel that they where discounted enough.
If you want more info, HSAbank.com has some. Good luck.