Firstly, you don't need a filter... if the tank is under 5g you don't need one.
You do need a heater... the house may be at 78, but room temp water will always be cooler.. also there will be fluctuations in the temp in the house, and anything too quickly and drastic will put the betta in shock and possibly kill him.
A heater will keep the tank at the right temp continuously and will avoid the risk of fluctuations. A 10-25w heater for a smaller tank is just fine.
The 1gal you picked out is JUST FINE. Don't need anything bigger. I would just avoid the bubbler as it may push the betta around too much.
Mirrors and bettas are just fine to do. In fact, people should be using a mirror as exercise daily for the betta (if the betta doesn't see other bettas on a regular basis). Three to five minutes once or twice a day is recommended to keep up muscles and get their blood pumping.
I would either get the tank you want (as you know how much you can spend and how much room you have).. if you want to upgrade then get one of the kritter keepers
, a medium is 1.75g, large is 2.75g (not 5g) which are plenty big enough and easy to care for.
As for decorations.. silk plants, glass items that don't have those sticker type decals, ceramics that have been glazed or plain.. just make sure there are no wires/metal of any type. You can build things (like glue rocks on a coffee mug, etc) using aquarium silicone.