I am by no means a power expert and can only give you my opinion based on what I have learned from other people and read in articles. Personally I only use a UPS. A good US should have surge protection built in, and should have a balancer to handle brown-outs and low power states. I currently use an APC UPS to protect my computer, and highly reccomend it. It has kept my computer running through a few brown-outs and safely shut my computer down during power outages that lasted more than 10 minutes.
From what I understand you never want to run multiple surge protection methods off of the wall. This means use just a Surge Strip or just a UPS (I'm not sure what an AVR is honestly). The reason you do not want to do this is because the second 'power protector' will be attemptng to draw more power through the first one which can lead to a trip in the surge protection, or cause damage to the first protector. It specifically says in the manual of my APC UPS to plug the unit directly into the wall and to NOT plug Surge Protectors into the UPS.
Another benefit to a UPS is that the Battery technically acts as a surge supressor as well as the power has to pass through the surge protection piece and the battery before it ever reaches your computer.
Again, I am no expert in this field, this is just what I have learned and use as best practice.
a surge protector does not protect again power blackout or brownouts, only a surge.
a battery backup combines a surge protector with a battery to protect against all 3.
for a high risk area a good battery backup is likely the wisest choice of action. keep in mind that they do not come cheap. a $200 model from apc will only power a typical mid to high level machine for 8-11 minutes in case of a power failure. this gives you enough time to shut your pc down correctly to not damage your components from a sudden loss of power under load situation.
since you seem to have many issues i would also not suggest leaving your computer or monitor on at all times. it would be best to shut everything down after you are done using them.
also keep in mind that a battery backup's battery does not last forever. you may need to replace this in a few years (depending on the MTBF and warranties) so be prepared for that eventualality. however, in your case it is well worth the investment.
currently i have only my tower hooked up which has a variable draw of between 200-450w. i do not have my monitor connected but you can read this link http://www.tomshardware.com/reviews/acer-s231hl-bid-del... for information on draw. without a monitor i get about 11 minutes of runtime and with a monitor connected the number drops to around 6-10.
at $210 this doesnt give you much in the way of usage time. however, it can and does protect your pc from brownouts and blackouts.