Pardon me if someone already said this - I haven't read all the responses.
I prefer turkey meatballs, but you are not likely to get the soft texture that you'll get with a fattier meat. My mom always made them with beef, pork and veal. I will not cook veal, but the beef/pork combo makes nice moist meatballs.
Since I started using turkey for meatballs I began using fresh breadcrumbs instead of the dry ones. I think this makes them a little softer.
I always brown mine in a skillet with a tiny bit of olive oil then plop them into the sauce. I only make meatballs if I am making sauce from scratch, as they need a lot of time simmering in the sauce to become tender.
Also, add some milk into your meat mixture. I don't know why this helps but I have always heard that it does. Be careful not to overwork the meat. I mix mine by hand, literally - I think this keeps the mixture from getting tough.
My grandma used to drop the raw meatballs right into the sauce, but as kids we didn't like them this way. We called them "Grandma's mushy meatballs".
~ house cat ~