Short version of my rambling: Go read this web page first -
http://www.6mmbr.com/gunsafes.html" onclick="window.open(this.href);return false;
Longer version that is more-specific to your situation:
It's less about price than it is about how secure the guns are. A third story apt presents a ton of problems for both you AND the bad guy. Get the most safe you can afford, but one thing I would suggest is a modular safe like the Dakota Interloc Safe. I have one of these (actually, two of them) and _love_ them.
http://www.dakotasafe.com/interlocxp.html" onclick="window.open(this.href);return false;. Zanotti also makes modular safes that are smaller, so it's important to shop around.
The Dakota safes are solid (weight about 500+ lbs when assembled), the interlocking plate system is undoubtedly pry-proof (more on that in a sec), and the safe is made from 12ga steel. Because the safe is in pieces, you get the package in 4 boxes, with the heaviest being the front door. Two strong people can haul that up to a 3rd floor apt, so you get the advantage of being able to move it yourself and not advertising, "Hey! I'm getting a heavy duty gun safe installed! I guess I own a lot of valuable guns". You can find safes like this at some dealers, or have one shipped to you for about $1000 from the manufacturer.
Now the slight downside: 12ga steel, as some safe vendors will tell you, isn't the thickest steel you can get, and will sell you on 8ga or 10ga steel, single mold forms (no welds/seams), and different fireproofing options. You have to weigh your situation with what you can afford and your personal preferences (read that gun safe buying guide I linked to above).
One thing I'll say about the high end safes, which will get very expensive: A determined thief that knows they are cracking a strong safe will bring a cutting (or plasma) torch and other tools, and will likely have carefully cased your habits and know exactly where your safe is. In an apartment situation though, you're more likely wanting something that will deter a pair of goons with inexpensive 3 foot wrecking bars. That means that _any_ safe must be a) Secured down to the floor and b) out of sight (tucked into a walk-in closet in your bedroom is best). Remember, a safe that isn't secured down is simply a heavy shopping cart for 4 strong thieves, or can be pushed over on the floor and then they can go to town on the front door with cheap pry bars (they can now use all their body weight as leverage if the safe is lying on the floor).
I don't fear guns; I fear voters and politicians that fear guns.