Looking for recommendations on a semi-auto rimfire rifle. What is your favorite caliber? What are the advantages of one caliber vs another?

Ruger 10/22 is always the first answer. It's the most successful semi-auto .22lr rifle in the history of the world for a reason.

10/22 all day, every day... I think half my safe is 10/22s in .22LR after I put all the kids guns in there. They just work, they shoot, and if you want them "your way" you can go absolutely crazy with after market parts, up to and including building a complete rifle without a single Ruger part.

Ditto and if you enjoy personalizing it in the same manner as AR's then it also has he most aftermarket parts for sure for rimfire but probably any gun ever made.

10/22 in 22LR, love mine

Another vote for the 10/22. I took a carbine model and a "rifle" model years ago and put the "rifle" 20" barrel with fiber optic sights on my carbine stock/action and have used that ever since and loved it. Sold the "rifle" action/stock with the carbine barrel and peep sights for the same thing I paid for the "rifle" model new, so it was a free upgrade for me. One of the few guns I will never sell.

another 10/22 fan, love mine.

Budget?

My budget is about $400

^what they said

10/22. As budget allows in the future you can replace the barrel (which you can do yourself) and get some real accuracy out of it. I think I have almost $600 invested in my 10/22 but the thing shoots lights out.

Yep.

$400 Ruger 10/22 bull barrel

another $400 on the scope, skimping on optics is a huge mistake