I'll also approach this from a "noob" perspective. If someone is asking what survival gun they should buy with their limited $250 budget, chances are they have a limited shooting background and probably don't own any other guns. So I'm assuming limited experience with firearms and no other firearms owned.
This is a question quite often asked by those new to the survival/prep hobby/lifestyle/way, and quite a legitimate one. The easy response to the question is "save up more money and buy a xxxx," which is all well and good, but fails to answer the question or be of much real help.
As in all aspects of prepping, location also plays a big part in what you need to consider first when looking at a firearm. If you live in a largely rural area, then a long arm or a shotgun would be a prime choice, in a more urban/suburban one, a handgun becomes ideal.
Additionally, there are a few compromises that one must consider when looking for a low-priced survival arm.
New/Used: When you've only got $250 to play with, there are fewer "factory-new" choices out there. They exist, but more choices come into play when used and older military surplus weapons are considered. Old/milsurp guns tend to be rough looking, oily and heavy, with no warranty and an unknown history. They probably don't come with a user's manual, and may have design quirks or intricacies that could cause confusion. Most work fine--some will need some work to get running (not what the new gun owner wants to deal with).
Bigger and Better: Speaking from experience, a $250 firearm is generally just a stop-gap measure until you can afford the gun that you really want. I bought a Ruger P95--the gun that I could afford--and traded it in towards a Glock--the gun that I wanted. While the P95 was a perfectly fine handgun, it wasn't what I really wanted. If you can wait/save a bit longer for the gun you really want, it'll save you money in the long run. But, guns hold their value fairly well--I took the Ruger out to the range several times and found out what I like/disliked in a handgun. When I traded it in, I lost all of about $25-$50 on the deal. Not a bad price to pay for the use I got out of the gun.
So, with all that being said, here are some of my favorites in the price range:
Rifles: Generally, the new shooter will find more enjoyment, entertainment, and satisfaction out of a rifle. They're just easier to shoot for most than a handgun, and the recoil is more manageable than a shotgun. Rifle ranges can be harder to find.
- SKS: Yep, shocking choice here. 10 rounds of semi auto 7.62x39mm goodness. Good out to about 200 yards. Fairly mild recoil. Fairly cheap ammo. Generally only available in Yugoslavian flavor at the $250 price range, though I'm much more partial to the Norinco. Yugos are heavy and unwieldy, with an unnecessary grenade launcher attachment on the end. Norincos are shorter, handier, and generally better finished and in better shape. Not a bad investment--SKSs are constantly creeping up in value as they become more scarce. Ooodles of accessories out there, if that's your kind of thing. You'll probably eventually want to get an AK-47, but the SKS makes a nice handout/backup/truck gun. Can pass for a "deer rifle" in some flavors. The classic "budget survival" gun for a reason.
- Used 30/30 Lever Gun: These pop up every now and then, some in perfectly beautiful condition. Not the ideal weapon to lay down heavy fire with, but a formidable rifle none-the-less. While not the latest in uber-tactical, a man can defend his home with one, take a deer, and so on.
- Ruger 10/22: The classic .22 for a reason. A great "first gun" and a welcome addition to any survival battery. Everyone needs a .22, even more so today with the high prices of ammunition. While not adequate for self defense, a 10/22 is a perfect gun to start shooting on. With an inexpensive 4x scope, they're capable of impressive accuracy. One of the most fun guns out there, and one you'll never get rid of. Great for training, practice, plinking, and small game gathering. If pressed, premium .22lr ammo is a lot better than throwing ninja stars, especially if it can be delivered en-mass (25 round magazines) and accurately. I can dump 25 rounds into a head shaped target at 25-50 yards without much trouble--not something I'd like to be on the receiving end of.
- CZ-52: I'm not a big fan of their looks, but these surplus handguns can be had for under $200, and carry the distinction of firing the 7.62x25mm round. x25mm surplus ammo can be had very cheaply--AIM Surplus has 1,224 round spam cans for $120. The round is known for its ability to punch through bullet proof vests. Not the best manstopper--small, fast FMJ rounds poke small holes in their targets. But hey, it's a handgun and it has nauseatingly cheap ammunition available--not a bad option.
- .38 Special Revolver: In this price range, you're probably looking at something from Charter Arms, Rossi, or Taurus, and you may be looking at something used. .38 +P is a respected defensive round, and there are a multitude of loadings out there for .38. Can fire miniature shotshell rounds for small game hunting if neeeded (though these have a fairly short effective range). Brass is easily saved for reloading or barter. Snubbies are harder to shoot, so unless the weapon is destined to be a CCW, look for a longer barrel. A solid working gun. If you can find one chambered in .357 in this price range, you're a good shopper--from my recent searching, .357s all land around $300+.
- Used Ruger Auto: These can sometimes be found around this price range. They're heavy and bulky looking, and the trigger leaves much to be desired, but they're workhorses. If you run out of ammo, you've got a formidable club to smack zombies and raiders with.