There are lots of guides on YouTube but this should suffice.
Costs are sort of just down to how into it you want to get. Kits range from $10-$300. I usually build ones in the $30-$80 range. You can get lots of fancy tools but really, just get a decent pair of sidecutters and a hobby knife (exacto or other brand) and maybe a sanding stick. I actually started with a nail polishing block that you can get at any store that has nailpolish.
Kit wise, really just start with a HG (High Grade) or EG (Entry Grade) that looks cool to you. If you find you enjoy the process more than the end product you can get into RG (real grade) or MG (Master Grade). All but MG are a 1/144 scale while MG is 1/100 scale. MG and RG are much more intricate.
As a last word of caution, the earlier RGs were not designed very well, each kit has a number, currently their are ~40 of them with the last 10 or so just being tiny MGs. The earlier ones can be great but need a bit more love to get right.
My personal favorite kit I have built is the RG Hi-Nu Gundam
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