A lot of good advice in these past 4 pages.
Just a few thoughts to add:
Do not worry much if the kitty is feline leukemia positive or feline aids (FIV - no relation to the human aids - it just mean immune deficiency) positive. No longer a death sentence in either case. A friend's cat that was feline leukemia positive for all of its 16 years ultimately died of something unrelated. I've cared for at least 2 feline aids positive cats. Good nutrition kept them well for a long time.
I agree - no clay litter. There are many alternatives these days.
For spay/neuter. You can go to the Friends of Animals website and learn what vets in your area participate in alow cost spay/neuter program. It's just a fraction of the usual cost. If no vets in your area participate call the state and see if it has a low cost program and who participates. In any case, you have lots of time before you have to think about that. Spay females at 6 months, males at around 8 months and all will be well.
If asking neighbors if they are missing a cat have them describe the cat to you, not vice versa, unless you know and trust them a whole lot. If the kitten came from a neighbor's unspayed cat, I would think twice, if they are letting their cats have kittens in a world where we're killing millions upon millions a year because there are not enough homes. Then this cat probably wouldn't get fixed either and more kittens would be forthcoming before long. I have rescued ferals that are as wild as any being I have ever seen and others who curled in my lap 5 minutes after I caught them so its docile behavior may not mean it's been in human care. If your observation that there may be a mother cat nearby is correct, then that mom is probably frantic looking for her baby. I would try to connect with that momma cat and see if she leads you to other babies.
Vaccinations - there is much evidence that we are over vaccinating pets like crazy. Some vets do not believe in any vaccinations. I split the difference and allow the first year vaccinations and then I don't repeat. Many vets believe the one vaccination conveys a lifetime of immunity. Not all agree but most now at least concede that annual vaccinations are serious overkill and frankly, just amoney maker for the vets. I also do not combine vaccines - too much stress on the cat. One at a time many weeks apart. My vets concur. I once had a kitten convulse and nearly die from too many vaccines at once - I began researching this issue from that point forward.
Depending upon your area, it's possible the kitten does not have fleas right now in which case the chemicals are not necessary at the moment. You can tell with a close inspection. The kitten probably does need a worming though.
Better stop here before I write a whole book!
You are so kind and caring to help this sweet little one - thank you.
JJ