I used to have a sentry safe similar to what those look like.
Mine cost right around 300 bucks with tax and shipping weight, with skid and stuff attached, was around 200lbs I think.
It is light enough to go on the 2nd floor and I moved it around myself, up and down a few steps and what not.
As for storage of ammo, I buy ammo by the case whenever possable. Generally it comes in a nice heavy duty cardboard box, thinking wolf ammo on that one, or I am buying surplus and it comes in nice metal ammo cans these days since I am buying the 308 at aim with 980 rounds per ammo can. I actually repack those back to their 1260 capacity so I get empty ammo cans for keeping loaded mags or other stuff in.
Right now I have some in a garage and some in my apartment. Neither will see huge temperature fluctuations but the stuff in the garage will be getting moved this fall I reckon.
Overall ammo handles serious temps pretty well if you research what military ammo might have seen temp. wise. Then again that might be part of why it got surplussed.