I love the idea of "military" .22s. I decided on the AR platform, and I've finally got a dedicated .22lr AR-15 that I get to shoot for the first time this weekend.
The AR is platform that I'm most familiar with, so here's what I know:
You can get Last Shot Bolt Hold Open with either a Ceiner AR-15 or a 10/22. Black Dog Machine makes Ceiner-compatible 27-round magazines with a LSBHO follower. This follower will lock the gun open, but it does not activate the bolt hold open on the AR. Therefore, the action will close when you eject the magazine. Single magazines will no longer drop free (in my case, I've heard of others where they did), but when coupled in a MagCinch, mine do. It would be pretty simple to weight up a single magazine so that it would drop free.
Also, Black Dog Machine is producing its 27 round magazine for the CZ V-22 upper and the M261 training unit. I don't know if these are compatible with the LSBHO. The website does not say that they are strictly limited to the Ceiner-based magazines, so I would assume that they would work in the other units as well.
BDM is also working on a WASR AK/22 30 round mag that should be out soon, if the AK is more your style. On their website, the owner states that he's going to try his magazine in a Ceiner AK conversion and see if it will function.
As far as gun choice, I chose the AR because I felt that it offered the greatest opprotunity for customization and fit. JP is now selling a kit that allows the direct attachment of AR sights, stocks, grips, and forearms while retaining the 10/22 action. Very interesting option, but I still prefer the AR safety and mag release.
If you do go the AR route, there's a couple of different ways to do it.
The simplest is to just get a Ceiner conversion and drop it in a 5.56/223 AR upper. The different twist rates (1/7 to 1/12) of the centerfire versus the rimfire (1/14 to 1/16), different bore diameter (.222 vs. .224) and the long freebore (about 2in) due to the .223 to .22lr chamber adaptor will be detrimental to accuracy, but you can still shoot .223/5.56 ammo through the upper, and I have read a review of just such a conversion that held 2" at 50 yards. However, I've also read reviews of conversions that didn't. If you're going this route, I would suggest a barrel with the 1/9 or 1/12 twist.
At the other end of the spectrum, you can get a dedicated .22 upper reciever. These guns have barrels with the proper twist rate, bore diameter, and have .22lr chambers. Due to the proper .22lr chambering, the chamber adaptor is removed. This is going to be your most accurate way to go. Common sources for these uppers are Model 1 Sales and Spike's Tactical.
The AR that I've got has a barrel with .22lr twist rate and bore diameter, but has a .223/5.56 chamber and uses the stock chamber adaptor from the Ciener kit. I got it from Kurt's Kustom Firearms, he's got pictures on his website of sub 1" 10 shot groups at 50 yards with match ammo, and 10 shot groups smaller than a quarter at 25 yards with bulk pack. Works for me. An advantage that I saw in going the route that I did was the ability to order a barrel with exactly the length and profile that I wanted. Also, by buying just the barrel and Ciener kit, I was able to completely part out my AR, and I didn't have to get rid of parts that I didn't want or need.
I think that rimfire action shooting is a great amount of fun. As much as I like both rimfires and actions shooting, I'd love a RIPSC where .22 rifles and pistols would be used.