Hi. I started out all-grain brewing on a small BIAB setup doing it on my stovetop. It was a good way for me to be sure I wanted to do it without initially shelling out much cash. It's easily done.
I used a 20L stockpot from Target or Kmart, bought a large BIAB grain bag from the local brew shop, get some heat proof gloves from the local hardware store as lifting the bag out and dealing with it with hot grain can be tricky without them, maybe a small hop bag for the hop additions or don't bother and chuck them in direct.
You should also get an auto siphon to get the wort out of the stockpot and into the fermenter whilst leaving behind as much as the trub as possible. And that's about it really, if you've been doing kits you'll have most other things (assuming you have a fermenter, a hydrometer etc).
Get a stick/ruler and measure the volumes in your stockpot (ie, add 1 or 2L of water into the stockpot, stick the ruler in and using a permanent marker note on the ruler where this is and keep going on the ruler until you get to the top).
Then you'll need to work out the volume of water you'll need for your grain bill. You can start out with some trial software (Beersmith, Brewers Friend) or some free software which limits your use (Brewfather).
And then just have a read about the process and ask lots of questions on the forum. Good luck.