I've honestly had decent luck with APC but also ran a lot of Tripp Lite. Eaton is decent. Using their calculator, this model (https://www.eaton.com/us/en-us/skuPage.5S1500LCD.html) would run for 71 minutes on a 100W load. It's going to be hard to get below $300 for an hour of runtime. You're going to want to target 1000VA or above.
homelab
Generally speaking, not APC unless its their pro grade, the charge controllers in the consumer stuff have historically been pretyy bad.
Their enterprise stuff went into battery subscription territory after Schneider bought them, and I dont even use their enterprise grade now.
Eaton is top tier with a price to match, and now owns tripplite as of... 2020ish? Maybe 2021?
CyberPower has generally been a great paperweight for me, but some folks have really liked some of their models, so couldn't say. At best I can say I like the housing designs of the ones I've gutted.
Must it be an APC or does any brand of UPS work?
Any. Im not picky. As long as I can replace the battery at some point its fine.
Have you thought about battery chemistry? LiFePo4 batteries last a lot longer because they don't degrade as much as lead acid during cycling, and they're better than standard lithium in that regard as well (draining them to 0 or having them charged at 100% doesn't harm the cells). Plus, they're a lot less explosively flammable than lithium.
They are more expensive, especially the rack mounted ones that allow for easy replacement. But goldenmate makes affordable ones that work really well! I have one that connects up to NUT via USB. I think they have that offering in smaller ones close to your budget, but you'd need to make sure it has the USB connection before going that route.
For example, this one is $229 usd and is 600W. You could run 100W on it for hours: https://goldenmateenergy.com/products/goldenmate-8-outlets-1000va-ups-lifepo4-battery-backup-and-surge-protector-with-nas-interface!
Eaton works well with https://wiki.debian.org/nut and I think the 5SC1000 fits your power needs.
https://networkupstools.org/docs/man/usbhid-ups.html