I love my AR-7. I bought it about three or four years ago, new, for less than $150.00. It is very lightweight; Will contain the barrel, receiver, magazine and a few rounds of loose ammo in the stock; And it floats! Also, even though the sights are- shall we say, remedial?- mine is surprisingly accurate.
Another thought, if you would consider more than just a rifle, Springfield Arms makes a combination gun called the M-6. This is the old Air Force survival gun with a .410 shotgun barrel under a small-bore rifle. I think the current offerings are .22LR and .22 Hornet. It's single-shot, barrel-break, hammer-select and has a weird trigger, but it does break down compactly, stores ammo in the stock and gives you more options than just a .22. I just bought one for about $200.00. I got the stainless instead of the parkerised model because I intend to canoe-hunt squirrel with it. I haven't shot it yet, but I intend to get to a range next week.
Another packable .22 was/is made by Browning with a detachable barrel and a tubular mag in the stock. These would be far from cheap, but Norinco made a decent quality (or so I'm told) much less expensive knock-off of the Browning.
Just to weigh-in on the handguns- Revolvers: Ruger Single-Six and H&R 999 Sportsman. Great guns both. Semi-autos: If I can find it in my heart to forgive S&W for selling out to HCI, my next pistol will be one of their new sporter series .22s. I spent a few hours on a range with several configurations at a vendor seminar when they first came out. They are comfortable, reliable, accurate and cheap.
Whatever you decide to get, get it while you can.
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Be Worthy