By heavily planted, I mean the tank needs to be pretty much a jungle. Not only is that necessary for shrimp, but it's great for the betta too. Trust me when I tell you that your fish wil come alive when he has a ton of foliage to play in. Here's a video of one of my tanks, showing what I mean. There's around 10 or 11 fake plants in this tank:
Quick Start is cycling bacteria that you can just put in the tank to start up your nitrogen cycle (the nitrogen cycle, as I mentioned, removes ammonia and nitrite from the water through a process called biological filtration). The nitrogen cycle will start on its own eventually, but that takes weeks, and you don't want your fish swimming in ammonia until then. One thing that can help you naturally cycle faster is putting the dirty, unrinsed gravel into the new tank with clean water. Gravel also accumulates cycling bacteria, so that's useful to transfer over. The water conditioner you're using is designed to remove chlorine (which is also deadly to fish), but it doesn't cycle the tank.
And yeah, a heater is a necessity. Bettas can't thrive at lower temperatures, and being housed at the wrong temp shortens their lifespans and makes them lethargic, less colorful and more susceptible to disease. When your tank is heated, you'll see so much personality you didn't before.
Walmart doesn't tell you this stuff because by and large, the staff just doesn't know. There's a lot of myths floating around about bettas that are just 100% not true. Further, most Walmarts don't have anyone managing the fish at all and the staff are completely apathetic to them. A lot of my bettas came from Walmart (I have 7 bettas!), and the deplorable conditions they're kept in there sicken me straight to my core. I wish I could take them all. I hate supporting the Walmart fish trade... but on the other hand I'm glad to have taken the beautiful fish I have away from that hell.
I can also recommend some useful cheap stuff to help you (plants, heater, etc) if you want.