Exactly what UPS are you looking at? You certainly don't need a UPS anywhere near that cost to run a single computer, particularly these days with LCD monitors. You're not trying to UPS a laser printer are you???
Unless it's a hybrid UPS with ferroresonant line conditioner, it's standby / float charging power consumption is pretty negligible.
The UPS to handle one computer will be about the size of a shoe box, and shouldn't be any issue to position along with the computer itself.
Not likely. My big UPS with my server rack in my garage is now about 10 years old, on it's original set of batteries and is showing no sign of any problems. The server rack loads it to about 15% capacity and just a couple weeks ago there was a power failure where it ran some 60 minutes on battery until I switched to generator power when the UPS reported 20 minutes of battery remaining.
Wildly exaggerated estimate, unless you're counting it's lifetime as 30 years and even then it's probably a high estimate.
What planet are you on buying new racks delivered? Racks are a dime a dozen used, often free and there is no reason to buy new unless you are building a showcase data center at which point you still need redundant UPSes, redundant generators, redundant air conditioning, access floors, etc.
It is by far, once you open your eyes to the real world and not some fantasy idea of a shiny enterprise data center.
Spend the $100 of a decent UPS at Fry's, Costco, etc., plug it in upstairs and get on with your life.
(The data centers I deal with have UPSes and generators rated in MW total capacity, and $250K/month electric bills)