That's great you've decided to upgrade your tank! I've had quite a few misconceptions myself when I first started out. I first had her in a tiny bowl without heater or filter, and I had plastic plants. :( That only lasted a few days though once I found this site!
What I recommend getting:
(Here's some pretty ones on amazon: http://www.amazon.com/s/ref=nb_sb_no...20silk%20plant
Real plants easy to care for: Anubias barteri, Anachris, hornwort
, Watesprite. Frogbit, Duckweed
Seachem Prime (Water conditioner used for water changes. Cost: $7-12)
Heater: 25 watt for 5 gallon tank, or 50watt for 10 gallon (A couple heaters most people recommend are Eheim Jagger heaters, or Aqueon submersible heater. They cost around $25)
Glass thermometer ($3 at pet store)
Hidey holes (something your fish can swim into and feel safe. There's a wide selection at pet stores. My betta loves the betta log. Usually cost around $6 for a medium-small one)
Gravel Vacuum w/ Bucket (Vacuum costs around $8, bucket $10)
API Master Test kit (this is for testing your water quality to make sure your betta isn't in bad water. You need a test kit to start cycling a tank. $20)
Good betta food (you could also buy her some treats if you like; bettas love freeze dried blood worms. $3-5)
It is best, as someone said above, to make sure the tank you get comes with a lid and light. ^^ Bettas sometimes jump from their tanks.
I might recommend getting an aquarium kit. They come with tank, lid, light, and filter. I recently bought the Top Fin 5.5 gallon aquarium kit, and it's been fine. Just make sure to read some reviews on the aquarium kits first. Some have awful reviews.
Good luck getting everything set up! :) I'm sure everyone would love to see a picture when it's all done!