do you already have a ups?
if not you can get a used one, provided it still works and charges a battery.
then to prolong the life you can get a sealed battery, like http://www.optimabatteries.com
make sure that the battery you are using is the same voltage as the one inside the UPS. i would figure they would be 12v..
you want a sealed battery because the others leak toxic fumes.
with a car battery you'll have a lot more time.
just for example.
the APC Back-UPS ES 550VA - APC BE550G has eight surge-protected power outlets total, with four offering battery backup. Backup runs for three minutes at full load (330W) and 13 minutes at half (165W)
the internal battery is 12v at 7ah (amp hours)
if you took out that battery and hooked up the yellow top optima battery you would have 12v at 75ah
the amp hours are the longevity of the battery from max charge to dead. smaller batteries that go into remotes, flashlights, or other devices are rated in mAH (milliampere-hours).
so in this example you would have about 10.71 times the "out of power" backup time.
so for 330w you would get 30mins, and at 165w you would have 140mins
you will be using about 171w, for safety sake well just round up to 200w
(Filter) The Fluval 306 runs on an economical 15 watts and has
a flow rate turnover of 255 Gallons / 1150 Litres per hour.
(Heater) Site says 150w for 55 gallon tank.
(Air pump) 6 Watts
• Rated for up to 15 air operated ornaments, filters, & airstones
you will want 3 of those yellow top batteries running in parallel. this will give you 225ah at 12v
at 200w you will roughty get about 5.62hrs of "out of power" run time.
if it truly only uses 171w total, you will see 6.57hr run time before the batteries are dead.
quick bit about batteries
in this example we will use a 3.7v lithium battery
when you charge a 3.7v lithium battery, they charge up to 4.2v, as the battery is used the voltage drops.
lithium batteries should never be drained past 20% battery life. (helpful tip to keep from replacing cell phone batteries)
lithium ion batteries usually have a protective circut on the battery if they are something like a 18650 or other size, cell phone batteries don't have them.
what this chip does is keeps from over charging past 4.2v and keeping you from using the battery when it gets below 2.7 - 2.9v
with the battery tip in mind, i would advise going 4 batteries in parallel.
this is if you will be running all of those items in the quoted bit above.
incase you arent aware, batteries hookeed in parallel, all of the + terminals are hooked together in one chain. all the - terminals are hooked together in a chain. this makes one large battery with the same voltage as one battery but a longer run time.
series is like a flashlight that uses more than one battery, what that does is doubles the voltage, the amp hour stays the same as using a single battery.
you can also run batteries in series then parallel them.. but this is unneeded info.
here is an illistration of the two "parallel" and "series", again with a 12v battery using the same apc unit you would run them in parallel
this is an expensive build, yellow top batteries are around $110 new.
you need sealed if you will have it inside your house so getting around a sealed battery IS NOT an option
if you would/could run the batteries outside, you could use a cheaper 12v battery that is not sealed.