Congrats on your new betta!
For starters, if you plan on being diligent with water changes, I don't think you need to go as large as 3 gallons. You certainly can if you'd like things to be a bit easier, but 1.5-2 gallons works just fine if you keep the water clean. To this purpose, I recommend you get an Ammonia and Nitrate/Nitrite test kit so that you can monitor those levels in your tank. If the levels are high, the water he's swimming in is toxic, and you'll need to tend to that.
I'm bad at advising on heaters, since I seem to need to replace one every month lately.
Most of my bettas don't have caves, but I buy fresh hornwort every week for floating cover and resting places. If I notice a fish is particularly panic-y or getting stressed, I give him more hiding places. Most of my fish are excited to see me though, since they believe I am some sort of magical food dispenser.
As for food, variety is great. I feed New Life Spectrum pellets, which are wonderful. I also feed frozen blood worms and/or brine shrimp twice a week. My bettas definitely prefer the frozen foods, but the pellets are more well-rounded nutrition-wise, so that's their staple. Fasting, I have found, is rather important, too. This helps to prevent digestion problems, like constipation, which is common in bettas. I fast my fish once or twice a week.
And don't worry about the impulse buy! My first betta I bought as a freshman in college, and I purchased him a 1/2 gallon home, as per the pet store employee's advice. I only changed the water once weekly, also through his advice, and my betta didn't last two months. After that, I didn't keep fish for a long time. I was confused as to what I could have done to contribute to the fish's death. It never even crossed my mind to get online and research for myself. I'm glad I've learned a lot about bettas and the need to research since then. :P
Good luck, and I hope you'll post photos of your new boy!
Last edited by inareverie85; 03-29-2012 at 10:13 PM.