Hello and welcome to the forum, and wonderful world of fish/betta keeping first of all :)
Alright, so, to begin.....your tank isn't going to cycle or build up any good bacteria without an ammonia source, either provided by fish waste or pure ammonia.
^There is a good site that describes how the cycle works, though you'll want to do research on which method you'd like to use; the choices being Fish-in or Fishless.
I would recommend fishless as it doesn't require any water changes and won't take as long to complete. The on;y downside is that you ill have to wait a while to purchase your fish....but in my opinion, the benefits far outweigh that one con.
Its up to you however, whatever you think you have time for....I'll warn you though, regardless of the method, you are going to want to find a Liquid Water Test kit. If you do fish-in, I suggest purchasing one, which will be quite a few bucks(you may need to save up for it if your really short on cash)...but if you do Fishless you may be able to get away with just taking your water down to your local fish store and getting them to test it for free, then save up and buy your test kit later on.
The ONLY way around the cycling process is to just remove the filter and do a 100% water change(with couple smaller partials in between)every week or so. But thats rather a pain in a 10 gallon.
There are lots of money-saving/cheap options for plants and decor....check around your local craft store. Using aquarium silicone you can glue together rocks for caves and such, the clay pots(plain, non-glazed)are less then a buck and also make great caves(you'll want to find a way to cover the little hole so your fish doesn't get stuck however).
The silk plants, provided they have no added scents or wires(sometimes wires can also be removed)can be used as well.
So long as you properly rinse and wash everything in hot/boiling water, lots of things you find in craft stores will work great, and are a LOT cheaper then anything you'll find in petstores. ;)
Bettas come from densely planted, dark waters in the wild....so they usually tend to feel more secure the more plants/hiding spots you have. So maybe grab some Aquarium silicone and head over to your local craft store xD
Hopefully this helps some :) And again, welcome!