Congratulations on getting this far!
As far as finishing goes, it depends on what character you want the materials to have, how much experience you have and how much time. Lacquer (and there are several types) encases the instrument in plastic, providing a solid finish that, if polished correctly, shows off the wood wonderfully. It takes a while to do, and involves lots of sanding.
French polish is tricky to get really good, but it's a beautiful finish and is easily reparable. If you go down that route I would advise getting someone who knows what they're doing to guide you.
There are many different types of oil finishes. One of the most straightforward to use is tru oil. It is easy to apply (rub in, wait a second, rub all the excess off, leave for a day, add another coat, repeat a few times) but the finish you get will only be as good as the sanded finish of your instrument. You need to get it perfect to get a great result.
RE grain filling: if You're using lacquer or French polish, yes you will need to grain fill. Pick a type and colour (I prefer thixotropic fillers), fill the grain then remove all excess filler from the surface. If you use a dark filler the pigment may well give you the darker stain you're looking for. If you want to do an oil finish you an leave the pores open, and you'll get a more natural look.
Hope that helps!
Most buskers aren't tramps... Most!