Bettas aren't really big fans of filters or currents. Plus they don't have a high bioload like goldfish. I would skip on the filter and use do whatever water changes are recommneded for a 1gallon. I do 2 a week, some people do more.
When you get the 5G, a sponge filter may be something to look into. you need to buy more parts but i wont coat more then buying a HOB filter. I think i'm gonna do that for one of my guys. Everytime I turn the filter on, next time I look at him his dark blue is faded to grey. Freaks me out every time too!
If you do go to walmart - I know they have tetra heaters for cheap but they suck. if your on a budget you may want to look at ebay or amazon. Better selection and possible cheaper then a petstore. Not always though. Some sellers charge an arm and a leg for shipping >.<
Now for his head - is that patch fuzzy? Are there any missing scales.leasions or anything like that?