Well, I'll take the *violinist part of the question (seeing as I am musician and play Viola and Piano).
Starter set for a violinist:
- Plywood Violin (Plywood is your basic type of wood for a wood instrument)
- Basic Rosin (nothing fancy, rosin makes a big difference in the sound you produce but it only compliments the bow).
- Basic Bow (Make sure you get a VIOLIN bow. Playing with anything else, even a Viola bow, is going to throw you off)
- Sponge Shoulder Rest (Don't need no fancy shmancy Tido, you can get a KUN should rest though).
- Beginner instruction books (I'd recommend the Essential Elements series as it will teach you all of the techniques basic -> advanced).
- Dampener (When winter approaches, your humidity is going to be thrown off and you need this)
So, making sure you know what this stuff is and how to use it:
The Violin is a wood instrument and therefore super fragile to climate and it's surroundings in general. You're not going to want to let any food, liquid, etc touch it at all. Keep it at room temperature and, if you want to go the extra mile and really invest in it's wellbeing, buy a humidifier. You only really need to worry about the humidity when winter strikes as you're in danger of the wood cracking and the spine splintering or the bridge slipping and and (oh gosh, scary thoughts).
Rosin in the stuff that you rub on your bow before you use it. Using a bow without rosin is useless. The bow is just really nice, clean horse hair just sitting there and look pretty. The rosin on it is what makes the hair stick and pull along the strings of the instrument, producing sound. If you get a brand new bow you're going to want to rosin for 5 minutes at least (takes a bit for it to stick on). From then on, you only really need 10-20 seconds if you're playing everyday.
You usually don't see the shoulder rest when you see a violinist playing. If you've ever held up the violin on your shoulder like you think it's supposed to be held you'll find it really uncomfortable and blistering even. What holds up your instrument in place, comfortably, is the shoulder rest. Your basic shoulder rest is a sponge one that you can just stick in and go. As you get better and desire better equipment, get out there and buy yourself a wood shoulder rest. Learning about your instrument will lead you to learn that if you get something like a KUN which grips your instrument with rubber feet that it'll dampen your sound. A wooden shoulder rest will help the sound carry through.
Dampeners. You stick them in water, ring them out, stick them in your instrument and you're good to go. Take it out before you play though.
Playing the violin is just one thing being said. After you learn your basics and your techniques - vibrato, shifting, etc, I'd encourage you a style that you want to play.
Anyways, wallotext enough. Feel free to ask me questions if you have more :3