My two cents: The 10/22 is a really good value. If you only want to spend $200 on a semi-auto .22 then the 10/22 is it. Pre-ban 25 round mags are available for the 10/22 and there are a million upgrades if you like to tinker.
In my opinion, the next logical jump up in price point for a semi-auto brings you to the S&W M&P 15-22 for $350. The AR platform has a little more versatility because it has a rail. The rifle includes flip up Magpul sights and you can easily experiment with different types of forward grips, scopes, red dot sights, etc and they just bolt right on to the rail. It's a newer rifle so no 30 round pre-ban mags exist. MA residents are limited to 10 round mags with this rifle.
Savage also makes some very nice bolt action .22's for short money. The design of the rifle uses a barrel nut to attach the barrel to the receiver so they're able to manufacture a pretty accurate rifle for relatively low cost. The Mark II series is very popular. The basic versions with a plastic stock and standard barrel start around $250. Higher end versions with wood stocks and bull barrels are also available.
I personally enjoy shooting a bolt action for two reasons. One, operating the bolt slows down my rate of fire which conserves ammo and saves a little money. Two, operating the bolt requires me to re-aim the rifle every shot. With a bolt action I aim, fire, cycle the bolt, aim, fire, cycle the bolt so it's 6-7 seconds between shots and creates more of a challenge and helps develop my skills (I'm not that skilled yet). With a semi-auto .22 there is almost no recoil and the rifle pretty much stays on target so I can rip through a 10 round mag in 5 seconds and keep a tight group. To me, it gets boring pretty quickly.
I personally own a Savage Mark II BV and a S&W M&P 15-22. I bought the Savage because I really loved the classic look and feel of a bolt gun with a wood stock. It's very solid, heavy, old timey and kinda romantic. I bought the 15-22 because it's the exact opposite of the Savage....Semi-auto, lightweight and modern but it uses the same ammo.