The common options for .22 LR AKs is the GSG AK47, the Romanian WASR22/AKT98, and Armscor AK22. I've owned an Armscor AK22 and currently have an AKT98.
If you decide to go for an Armscor AK22, it is a decent option if you are on a budget. These guns are cosmetically modified Squires Bingham M20 rifles that Armscor has been making for awhile now in the Philippines. It is really a very basic tube receiver semi-auto blowback rifle at its heart. I have seen a lot of reports of good function on these, however mine wasn't the best. Like almost all .22s it was ammo sensitive. Mine was just too unreliable for me.
Magazines can be hard to find but I got some directly from the Armscor USA distributor. You can get some 10, 15, and 25 round magazines. The 10 and 15 rounders are the best magazines and are actually M20 magazines with a cosmetic body. If you are looking for an AK style plinker for cheap, it can be a good option. However, it has a few training issues if you are trying for full 1:1 training features of a centerfire AK. First its magazines aren't rock in and out like a normal AK, also the mag latch is on the magazine body. Unless you own a milled AK, the stock angle if a little off and length of pull are off from a standard AK. I had to modify an airsoft AKM/74 style stock to get the feel of my stamped AKs. The safety is definitely takes less effort to use than a regular AK, but it does do a good job replicating it other than that and comes with a bolt hold open notch.
The Romanian WASR22/AKT98 is has some very good and very bad points. The good thing about it is that it is built on a centerfire AK receiver which means many interchangeable parts, like furniture and safeties But it takes a lot of tweaking to get running reliably. Also it has a tendency to blow out the extractor system parts when it has a out of battery detention. Luckily, a .22 LR Ka-Boom doesn't really hurt a shooter with proper eye protection nor does it hurt the gun, save the extractor system. Finding replacements for the extractor, extractor spring, etc. can be extremely difficult and there are many otherwise perfectly good WASR22 platform guns that just need an extractor. Unfortunately, there is no one that is making new production replacement extractors.
There has been talk of a third party bolt, first by Black Dog Machine and now by an AK machinist that goes by TurboThis. The bolt would use commonly available 10/22 extractor and save many of these rifles from the brink.
The blown extractor problem can be prevented by using round nose ammo that fully feeds into the chamber and by overall tweaks like the extractor tension, plugging the non-functional gas tube, and changing to a standard AK dust cover.
Overall though if you want a true .22 LR AK, this is the way to go. I am pretty happy with my AKT98. It is actually the AK I shoot the most since my local range doesn't allow centerfire rifle cartridges. Since they are so close to regular AKs and are no longer imported into the United States, they tend to be somewhat expensive. Expect to spend $350-$500 for a functional rifle. Magazines can be pretty affordable. The Black Dog Machine 30 rounders are $25-$30, 10 rounder metal shell mags for $10-$25, and short 10 round polymer for $12-$18.
I feel that these three are really the best options for .22 AKs. I 'm not a fan of the Krinker Plinker 10/22 conversion due to cost plus the non-standard AK safety and rear sight. The Saiga .22 LR may finally be imported someday and blow the rest of these out of the water, but it hasn't happened yet.