First thing, 5 gallon is a good size for a lone betta. I wouldn't use plastice wrap as it will stretch real easily and possibly melt from the lampand become a hassle more than a help. I would suggest getting some plexi-glass cut at your local hardware store, try Lowe's I think they'll even cut it for you.
as for heaters i would try something like this: http://www.amazon.com/HEATER-Aquariu...585661&sr=8-13
or this: http://www.amazon.com/Tetra-26447-Su...585661&sr=8-14
wich is what I use. make sure you have a thermometer though so you can always monitor the temperature.
If you don't want to use a filter, you don't really have to, just do partial water changed one or twice a week, and to a total clean sweep once a month or every 2 months, depending on the dirtyness, you want to get a water test kit to keep an eye on the ammonia and ph level, and also Nitrates and nitrites. but if your cleaning regulary it shouldn't be much of an issue.
As for decorations, plants are great , and hides/caves are really good too, make sure there is plenty of surface area though for them to come up and get air. try to switch them around or change different ones to keep them interesting to your betta. They like color and motion.
the pebbles would be pretty just make sure they're clean, i's put them in bloiling water for a few minutes then rinse in cold.
as for money saving tips, i try to buy things on amazon, rather than petstores, the retail markups on tank deco is rediculous! haha i saw a pot/cave thingy at my local pet store for 27.99 i was like what the!
as for where to purchase your betta, in my opinion its completely up to you, some people won't buy from wal-mart beacuse they're poorly taken care of, Lots of people have gotten bettas in bad shappe and really saved them. I got my Elton at a pet shop I used to work at, I always give them all my business :-p
I think i answered everything lol good luck in finding everything you need, if you have any questions just ask :-p we're all more than happy to help ;)
EDIT: if you've never owned a betta before, you're in for a pleasant surprise! Lots of them are super smart and have different personalities! Just keep them warm, clean and happy and I'm sure it'll have a long happy healthy life for you both to enjoy!
EDIT #2: haha you didn't ask, but I forgot to mention diet. Bettas are carnivorous so make sure you give them as much good quality, and as much variety of foods as you can. It keeps them healthy, brightly colored and keeps them from getting bored. Brine shrimp and bloodworms are great for them. a lot of people here feed Hikari brant Betta Bio-Gold pellets. They're good too. It just depends on your betta too. Just keep trying different things, but don't overfeed :D