That’s great....
Now you started a thread for all the “Know it All’s and soon their cousins the “Know Everything’s” and their neighbors the “Have an Opinion ‘bout everythings” will be showing up.
I’d help you but my reference library of armaments fell over board, into the Monterey Bay, while I was cleaning my guns and gutting fish...
If you’re looking to burn a brick of bullets in an hour, the Ruger 10/22 is the gun, with available 25-round banana magazines. Spend 45 minutes thumb-loading the mags, and 2 minutes emptying them.
If you’re looking for a super sweet, perfectly balanced .22 that can mount a scope and pick a flea off a squirrel’s nose from 75 yards, the Remington tube-feed 552 Speedmaster is the gun.
Wrong. We have more opinions about guns than any other group of people on the planet, but you have to realize that some of those opinions are in fact anti-knowledge. Consequently, when you put knowledge and anti-knowledge together in the same thread, the result is potentially catastrophic. In particularly egregious situations, you may leave a thread dumber than when you went in.
Any shotgun can shoot slugs, but when I put a rifled choke in my Rem 870 I get better groups at 100 yds than without it at 50 yds.
For a .22 rifle, it's hard to go wrong with a Ruger 10/22. Good right out of the box, plus there are plenty of aftermarket stocks and accessories available to make it better and more personal.
12 ga. slugs put really big holes in targets. Shoot the .22 first.
Mossberg 500 or Remington 870 are both quality home defense shotguns for under $400. Things to look for are shorter barrel, 18.5” to 20”, capacity 7+1 and ease of use, i.e. point and shoot. Would not recommend slugs in the house as they will penetrate a car door at 50yds, dry wall offers no protection for innocent bystanders, i.e. children in the house. Get some 00 or 000 buck shot. BTW, don’t waste money on the fancy packaged HD ammo being sold at $25 per box of ten. Plain old Walmart $3.25 000 buck will do the job.
Both the Ruger 10/22 or Marlin 60 are great .22LR plinkers that can be used to take small game and varmints. Both rifles are almost universal in usage, have many aftermarket parts available and shoot quite well for inexpensive guns. Keep in mind that 50 - 100 yds is all you are going to get out of a basic .22 round so if you need more, start thinking about a .223 or .308 platform.
Good Luck
Remington 870 Shotgun. Very reliable.
If you are looking at 22...then I would suggest the Ruger SR-22. For the money this is the best 22LR rifle you can pick up. Basically gives you an AR platform for 22LR.
You can pick up a really good Leupold scope for the SR-22, something like an AR 3-9X40 for about $350.
But if you really want a decent varmint long rifle then I would suggest the Remmington 700 with a decent scope - in fact I would spend as much on the scope as the rifle.
For the 700 I would look at something like a Leupold VX3L 3.5-10X56 - that one will run you anywhere between $850 to a grand depending on what options, etc.
You are going to want a really good scope, especially if you are past that magic age of 45 where your eyesight is starting to take a hit. Iron sights are good to learn on so you have the experience but if you are really interested in personal protection and the ability to hunt to survive you want every advantage and the scope is just as if not more important than the actual gun.
BTW...your ammmo selection is going to be very important. There is a lot of crap ammo out there that jams, etc...and is really dirty (means a lot more cleaning).
Winchester, Hornady and Federal all have excellent premium ammo. Winchester Ranger is really great, never had a problem.
Of course for target practice any Winchester ammo seems to work well.
You will want to research on www.gunbroker.com and see if you can find a local private seller - that is the best way to purchase - depending on what state you live in.
Also www.luckygunner.com seems to have ammo most of the time albeit it can be pricey but at least you can get it.
You don't want a .22LR or semi-auto for varmints. The speed of the bullet is too low. This has several issues. First, distance matters a lot, and in the field you will see small game (or nongame, like ground squirrels) at all distances. Second, the .22lr hit may be not sufficient for an instant kill.
Thirdly, semi-auto rifle is not usable in the field because of the flying brass. I personally don't even take magazines with me. I load the round into the chamber by hand, close the bolt, shoot, wrap my hand around the ejection area and open the bolt. The case falls into my hand, I put it in a pocket. No littering in the field!
Besides, rarely a follow-up shot is possible on a small game. If you miss it's not by much, and the rodent in question is probably hightailing out of there so fast you can't even see it through the scope. Shooting at such a target through the scope is dangerous; shooting at it with iron sights is possible, but not very effective (the distances are too large, and the targets are small.)
I have a .22LR and .22WMR, but these are not my preferred varmint rifles. Not even .223, which I also have and like. The best one is .17HMR, and that's what you want for small game (up to a coyote.) 17HMR has very low recoil, allowing you to see the aim point through the scope after the shot; my .223 doesn't allow me that luxury, and I don't have a spotter. The 17HMR bullet is very fast (about 2500 fps) which means you can shoot at anything from 10 to 150-200 yards without touching the scope (just correct for parallax for very close shots, and hold over the aim point a bit for longest shots.)
The effective range of 17HMR is also better, about 200 yards. The ammo is not expensive, and it looks good too :-) There is lead-free ammo too, and I use it where I must, living in CA. The V-Max bullets which I kind of like stay entirely within the rodent (one hole in, zero holes out - all the energy is spent within the target, just as you want it.) The bullets are very effective, and almost any hit is a kill (though of course you should aim at areas that are prescribed for the species that you hunt; for squirrels it's the neck.)
I put about 300 rounds of 17HMR into one pocket, and that's enough to walk around for several hours. You can't do that with .223 rounds; you'd need a golf bag or a backpack :-)
So if you really want a rifle for varmints, please consider 17HMR. But of course if you want a semi-auto .22LR rifle that can also be used to shoot in the general direction of varmints, then that's a different story :-) Just remember that CA's Fish & Game code forbids scaring the game :-)
I’m late to the party but...
for the .22 a Ruger 10/22 is hard to beat.
My shotgun is a 12 gauge Mossburg 590, but I don’t shoot slugs.
May I suggest H&R/New England Fireamrs which have a combo rifle/shotgun.
They are single shot, break action weapons.
They are inexpensive and you may add sifferent barrels in different calibers with the center fire combos. Now owned and made by Marlin, they are a good quality, low cost option.
Rossi offers a similar package, the the H&R/NEF have better sights IMO.
Just an option if you do not plan on being the field very often for hunting
May I suggest H&R/New England Fireamrs which have a combo rifle/shotgun.
They are single shot, break action weapons.
They are inexpensive and you may add sifferent barrels in different calibers with the center fire combos. Now owned and made by Marlin, they are a good quality, low cost option.
Rossi offers a similar package, the the H&R/NEF have better sights IMO.
Just an option if you do not plan on being the field very often for hunting
I’m glad you asked. Now I don’t have to start my own thread.
Don’t mean to hijack your thread bjorn, but I could use some advice myself. Would like an inexpensive scope for my 10/22. Any suggestions?
A couple of years ago, a similar thread led me to the Ruger 10/22 and the Remington 870 express synthetic 7-round.
I certainly won’t claim to be an expert, but I am happy with each. FWIW.
I love these threads.
I recommend--- and American 180... 
as a neat varmit plunker.
About 10 grand here!
And the .22 ammo is so... 
cheap!
If there is a Red X go to http://en.wikipedia.org/wiki/American-180