Melbasha, I didn’t see a reply to your questions about a child’s violin, so I’ll see if I can help. First, you should know that I am a beginner, so take my comments with that in mind.
Ask a local instructor about how old a child should be. I’ve heard answers as young as 4 and as old as 11, but I think it would depend on the child. The Suzuki method believes starting children very young is advantageous. Try reading about the Suzuki method.
I believe there is a forum on violin sizing here. If not, Google “what size violin” to get a chart. Some places will rent violins for small children down to 1/16 size. Rental may make sense so that, as your child grows, you can trade for a larger instrument.
As for yourself, rent a quality student violin which should run between $18 and $30 or so, at least until you find out 1) if you enjoy playing and 2) what type of violin you would like to get. That way, you won’t get stuck with a crummy instrument that is hard to play and sounds bad. I did that with an acoustic guitar and quit playing for years because I thought guitars were painful to play.
I found that, after a month or so of playing, I had a definite preference for the sound of certain violins. I may not be a competent player, but I know what sound I like. Unfortunately, the violin I love is outside of my price range right now, but I have found a few in my price range that I like a lot.
Michael, who owns this site, is very helpful. Try the chat feature on this site to ask your questions. I’ve found the people on this site to be helpful and friendly as well.
Good luck and have fun!