Okay. I'm going to stray from my friends here who have given you some great recommendations.
Why are you tripping breakers?! Especially so often that you're looking to get a UPS?! Is it an actual fuse as stated or a breaker?
If it's a fuse, make sure that you are only using the proper rated fuse. Don't blow fuses then upgrade to a higher amperage to stop it from blowing. Same with a breaker. If you have 14 AWG wire then 15 amp is the highest. 12 AWG then you can go to 20 amp. Do NOT go higher! The point of a fuse or breaker is that they will sacrifice themselves. If they don't do that, then the wire sacrifices itself and then your home goes up in flame. Don't do it.
If you have a breaker, they do wear out. Trip too often and over time they trip too easy. Replace old/worn out breakers with equivalent. Again, do NOT upgrade to a higher amperage. Pay attention to the brand of your electrical box. Square D is a common brand as is GE, Eaton, etc. When looking at your panel, note the manufacturer. Look for breakers from the same manufacturer. It's not a problem if you get the wrong brand. It won't fit and you'll have to go back to the store to get the right one. I also recently found that my Square D is older and not compatible with their new style.
How do you know if your circuit is 15 or 20 amp? Depending on the age of your home, Romex makes it really easy. If you look at the insulation for the wire, is it yellow or white or...? White Romex is 14 AWG or 15 amp. Yellow is 12 AWG or 20 amp. You can really feel the difference too when trying to bend the wire. 12 AWG is really stiff and tough to stuff in the outlet box. 14 AWG bends really easy. If you have cloth covered wire, 15 amp at most. Pay attention to all of this.
Alternatively, get a licensed electrician in your home to figure it out. Do NOT let this go on. Do NOT! Fix the problem instead of masking it. It could save your life. If you have too many things plugged into a circuit, try to move things around. There are a lot of rules when dealing with electric so take the time or hire a pro.
When our house was built, they wired two bedrooms and a bathroom together. For a while, with all of my computer gear in the spare bedroom, when my wife turned on her hair dryer... POP! everything went out. We hired an electrician to wire most of the bathroom on it's own circuit. Problem solved.
Back to UPS recommendations, I use 1500VA UPS similar to what is listed above. I tried to buy ones that have a true sine wave or as close as I could afford. True sine waves UPS' are expensive but they treat your electronics much better than cheaper ones. I don't use the UPS for my computers. Instead I use them on my networking gear. We have lots of minor power outages in my neighborhood. Sometimes just a few seconds to a minute or two. On occasion we have a few days of power outages. With frequent power blips (as I'll call them), I get tired of resetting and powering on all of my network gear. Modem, router, switches, WAPs, etc. Having the UPS keeps them running with a power blip and thus I don't have to run all over the basement resetting equipment.
Edit: Space heaters are really bad for this. A single space heater can easily use 1500 wats. That's almost all of the headroom for a 15 amp circuit. This leaves you with 300 wats for other things. Anything that turns electric into heat uses a lot of electric. By reducing heaters, your clothes iron, incandescent lights, halogen lights, etc can reduce the load on your circuit and help out.
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