Hey PB

All good info here on your question. You might want to pick up a thingy called a "Kilowatt." These let you monitor the circuit "real time" and tell you the wattage (and how many amps is being drawn) for each peice of equipment. Keep in mind that it is not going to tell you how much of a load is on the entire circuit, so there is still a danger of popping a breaker when something else on the circuit is turned on.

Like the others said, you are probably ok and will not burn the house down.  If you are not picking up any hums or radio interference, again you are probably ok.

https://www.amazon.com/P3-P4400-Electricity-Usage-Monitor/dp/B00009MDBU/ref=sr_1_1?ie=UTF8&qid=1482071958&sr=8-1&keywords=killowatt

PS if you can afford it, you might want to also pick up a "circuit detective" that will allow you to trace the outlets on a particualr breaker. It is a bit pricey, but you can use it to troubleshoot in the future.

https://www.amazon.com/USA-Tools-More-Circuit-Detective/dp/B01M16X6B0/ref=sr_1_5?ie=UTF8&qid=1482073379&sr=8-5&keywords=circuit+breaker+detective

Take care,
h

The only things I connect to a UPS is the computer and screen, so I get enough time to save stuff and shut down cleanly or hibernate. Many UPS units can't reliably keep a PC plus screen alive for more than a minute or two, despite what the manufacturers claim. It's always a good idea to hook stuff up to the UPS then kill thenpower into the UPS to check it does what you expect, just like it's a good idea to restore a backup sometimes to check that the backups you hope will save you from data loss are actually any good.

Laptops don't get a UPS, they already have a battery.

Everything else gets just surge protection in case of power spikes or nearby lightning ground strike.

I've an insane looking number of wall warts in use, something like 16, and the ring main those are on also carries some other stuff in other rooms. Just because there are two separate sockets a distance apart, don't assume they aren't linked as part of the same ring that goes back to a single fuse/breaker on the mains distribution unit, typically somewhere around 13A in the UK, with typically an 80A building fuse in a domestic premises meter.

The total draw for the wall warts is around 3.5 amps by the way, many are rated at 500mA or more but the synths/fx/drive they're attached to draws nothing like that much. The rating on the wall wart tells you the maximum it can deliver, not how much it's actually being asked for which will always be less.

+1 to tlw post. 
Your plan to continue using the UPS and just add a good quality surge protector for the rest is what most do in studios. 
Most UPS I've used have 3 outlets that use the battery backup and a few more that are just surge protected. 
Of everything in a modern studio your powered monitors or any guitar amps will be the only big users. Your computer will come next, but the rest of the gear is almost always wall wart driven and not an issue. 
More important would be to know what else in your household is sharing that breaker. 
But if it doesn't pop the breaker all is good. there's no danger with the way any house built in the last 40 years are wired unless it's owner built or ? and someone didn't follow the code.