We aren't here to take sides on the time-old debate about cooking meatballs. There are pros and cons to both roasting them and simmering them. Here are some considerations.
Roasting: Think of the meatball as a big hamburger. It's beef based, so you can serve it medium if you want. Take it too far, and it's going to be tough like an overdone hamburger.
Roasting a meatball can give it a nice crust and a tender inside when done properly. Roasted meatballs should be served immediately after roasting to provide the best experience.
Simply oil a sheet pan or any oven proof skillet. Preheat your oven to 375 and roast, turning once, until internal temperature reaches 125 degrees, but no more than 150.
Remove the meatballs from the oven and let rest on a wood cutting board for approximately 5 minutes before serving. They should continue to cook about 5 degrees. 125 will provide medium to medium well meatballs; 150 will provide well done.
For an extra crisp on the surface, consider turning on the broiler and moving the cooking rack near the top of the oven for the last third.
The downsides of roasting: splatter in your oven and potential to dry them out.
Simmering
Simmering a meatball in sauce enriches the sauce and provides a tender, fully cooked meatball. You won't need to worry so much about specific temperatures.
Start by getting a skillet hot, adding some oil, and browning them on all sides. Then there are two approaches to finishing:
Simple Approach: Move the meatballs to a clean saucepan just big enough for the meatballs. Cover in tomato sauce and simmer until tender.
Doctored Up Sauce Approach: Be sure you are using a skillet, not a saute pan, to brown the meatballs. Remove the meatballs to a plate and drain off the grease. Over medium flame, deglaze the pan with red wine, scraping the bottom clean. Reduce the red wine until almost gone, then add tomato juice, approx a cup. Reduce by half and add your meatballs back and your tomato sauce. Let simmer.
If you want to add mushrooms to your sauce, clean your mushrooms by removing the stem (saving for the stock pot) and slice the mushrooms. Over medium heat, add oil or butter to a skillet and add sliced onions and mushrooms to the pan, sauteing until tender. Fold into the tomato sauce and simmer with meatballs.