Well everyone and their brother has an opinion on the best guns for a post apocalyptic world (PAW). You know what they say about opinions so I just felt I have to throw mine into the ring. Now keep in mind that this is "on the cheap" and is also "my opinion".
Let me preface this by saying if you haven't taken advantage of the FFL C&R yet you are foolish. It is easy to get (if you aren't a criminal), cheap and did I mention you can order qualified guns right over the Internet and have them delivered to your door. The guns I am going to list here are ALL C&R eligible and can be ordered and delivered if you have that magic piece of paper.
Ok so here is the list:
Mosin Nagant 91/30/M44/M38/etc - Ok This is the epitomy of the survivalist gun. They are cheap, built like tanks, powerful as all hell, accurate and most importantly plentiful. It is the sheer number of these that are available which is the biggest benefit. The law of supply and demand say if there is a lot of supply with less demand, prices are cheap. This is hands down the cheapest survival weapon out there and in some cases I have seen them listed for $59. They are chambered in 7.62x54 which is a big whoop ass round that travels far with punch. The down side is these thing kick like a mule. Bolt manipulation can also be a chore on these things. That being said they are a decent gun and the price is right. The magazine capacity is 5 rounds fed by stripper clips. Honestly if I am being attacked by the zombie hoards is this the weapon of choice for me? Not really I prefer something in semi-auto, which leads me to the next gun on the list.
SKS - I like to think of this as the precursor to the AK-47. The gun is semi-auto and chambered in the cheap and plentiful 7.62x39 caliber. The gun has a 10 round magazine fed by stripper clips. There are many varieties and they all have their pluses and minuses. I have a Yugo M59/66 which some people will tell you suck because it doesn't have a chromed barrel. Well the Yugo make up for that in girth, everything is bigger and heavier on the Yugo. The other varients are Chinese, Russian, Albanian, etc, it is up to you what you select. I have seen these for between $150 and $300+ depending on the condition. I got one in brand new condition for $275 and I think it was a great investment. I personally for the money think this is your best bet if you are in need of a SHTF gun on the cheap. There are a ton of accessories for them available including detachable magazines and replacement stocks.
Lee Enfield - This gun comes in many variants, I would go for one chambered in .308 (well 7.62x51 really) because it is a common albeit expensive round. They do warn you .308 could generate higher pressures than the NATO round but I am not an expert so do your homework. This gun is one of the most successful military rifles ever in production. The bolt is one of the smoothest you will use and these guns can be fired at an extremely rapid rate. The Brits used to call it the "mad minute", they would lay down so much fire in a minute that enemies often thought they were being fired at with machine guns. Personally if bolt-action is your thing...I would take a Lee Enfield over a Mosin...but again that is just my opinion (No hate mail please). The Lee Enfield also has a higher magazine capacity at 12 rounds vs. the Mosin at 5. They run the gambit but SOG has the 2A version in .308 (12 rounds) for about $169.
There are a few more namely the Mauser but I am not a big fan of uncommon calibers...this is a decent list to start from. I can't stress enough to folks that they should try and get their FFL C&R, it opens up a bunch of avenues for purchasing cheap firearms, delivered right to your door.
...that is all.
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