I haven't bought or researched these in many years.  Can the hive save me some time and point me in the direction of something just above economy level?

Need to run satellite modem, router and camera system during power outages.  I haven't built up a power bank yet, but that will follow.  For now, a single deep cycle and charger I already have will be the source.  I just don't want to waste money on a stand alone UPS.  I'd rather have something I can build upon.

ETA:  Although I've heard Starlink pulls about 100w, so far, with a cheap wired camera system and starlink both running, my kill-a-watt says I'm averaging well under 100watt combined.  Closer to 70-80 (24hr sample).  I don't have a problem running a way over that (2k range) as I'd just find something else to power too.  But it's looking like 300-500 would be more than sufficient.  But this can be modular for sure.  Small pure sine wave for these, old school 2k I have sitting idle for lights, TV, fireplace blower, ceiling fans.  Hmmm...

I have a Xantrex 1000W inverter in our camper.  I had a cheaper (non sine-wave), and it was fine on some things, but the microwave didn't like the square wave.  Everything works well on the Xantrex.

Indeed, get a pure sine wave inverter. They get along with everything. They cost more, but they are easier on your stuff.

None of those items sound very power-hungry, or picky about power quality.

If you have a cheap "modified sine wave" inverter laying around, you might consider trying it with those items to see if they work OK with it.

"Pure sine wave" inverters are fine for some applications, but they're typically not as efficient (particularly when running lightly loaded), and they are a LOT more expensive.

Also, using a large inverter to power a small load is inefficient - a lot of battery energy gets wasted just keeping the inverter running.

I have a small Magnum Power Inverter,   was made in Washinton.
MS1012, will push a real kilowatt continuous. Also charges at a solid 60 Amps with AC input, auto transfer switch.
They seem to hold up well, mine has been running 10 years as battery back up power for furnace and security systems.

This right here. You need to find the actual wattage for what you'll be running and size the inverter appropriately. None of that is going to have a huge start-up requirement like a fridge or an A/C unit, so I'd shoot for an inverter that's rated just 10-20% more than your actually pulling.

Magnum, Samlex and maybe Xantrex. I used to like the Prosine.

I went cheap.  Renogy.  Haven't regretted it yet.  In the end, the batteries and solar cost much more.  The system is modular, that's what I wanted.  Well, and to work.