.22 rifles are great, and you will not regret purchasing one over a Mosin.
I have several .22 rifles. In many ways, my favorite is my Marlin 795. The 795 is an auto-loading, detachable magazine, synthetic-stocked rifle. You can get a 795 all day for $99 after rebate. The 795 has been my project rifle in many ways. When I say project rifle, I don't mean that I have swapped barrels and stocks and every other part on the gun. That is the kind of thing I (and everyone else) do with a 10/22. I mean that I have made a concerted effort to really make this rifle mine, modifying comb height (took less than $20 and 10 minutes), changing the sights to Tech Sights, polishing up parts for aesthetics, and making the trigger just how I want it. It shoots cheap bulk ammo very accurately, and as a bonus, came with sling swivel studs already installed.
The 795 is not perfect. Out of the box, the trigger is too heavy. Also, the integral rail for mounting scopes/receiver sights was not milled correctly on mine. I fixed that with a shim. The stock iron sights suck...but they do on basically every rifle.
However, the rifle gets little to no credit for what it is - an accurate, inexpensive, lightweight rifle with a trigger that has potential. My rifle has a comb kit, tech sights, sling, and 4 magazines. I have ~$240 in the gun. ~40 of that is magazines.
The 795 is the rifle I shot rifleman with at Appleseed.
A different option would be a Savage Mk II.
This is a great bolt action rifle that is very accurate and ergonomic. You can get a "taxi cab" version or a Cadillac with this rifle. Lots of options. Slick action, accurate barrel, inexpensive magazines.
I do not like the magazine release on this rifle, but basically love everything else. If you don't like the Accutrigger, you may not like this rifle. I do like the Accutrigger, and love this rifle (actually, I have the 17hmr version...but they are the same).
Of course, there is always the Ruger 10/22. The 10/22 is the tinkerers rifle of choice. I think they are perfectly accurate. My wife's 10/22 is the most accurate .22 rifle we have. However, it is not very accurate with cheap bulk ammo. I shoot much more expensive ammo through it. $5 a box of 50 (which is still cheaper than Mosin ammo). The 10/22 starts out at about $200-240 for the carbine version. But you will inevitably end up spending more money getting a cool stock, maybe an aftermarket barrel, etc.
I think the 10/22 magazines are pretty cool, and they aren't too terribly expensive either.
The stock iron sights suck, but can be easily replaced with optics or Tech Sights/Williams Sights.
My wife's rifle greatly benefited from floating the stock, sporter-style barrel. I put it in a Boyd's stock that she picked out.
Buy a 91/30 and you'll love it. First of all, please don't worry about mounting a scope on it. With open sights, a heavy trigger and recoil to purposefully not flinch at, you will become a MUCH better shooter than you are today. Practice seriously, while having fun!!