Thank you one and all for your advice.
I decided to buy an APC 390 watt/620 watt surge Smart UPS unit (SC620), which regulates the power, using the battery power momentarily when the generator power surges too low or too high. Not a perfect solution, because there is always some risk with these unregulated generators, but their tech support said that this should work on the low power draw that I'll be using.
I tested the current draw on all my computer devices, and was surprised at how little they actually use. My laptop runs at 12 watts, my router and modem run on 12 watts combined, and my inkjet printer runs on 18 watts (my laser printer is over 600 watts, so I won't be using that in a power failure). I can actually run my office at a survival level from a 100-amp-hour deep cycle battery with a 75-watt inverter for quite a while, it turns out, and that may be my first line of defense, because that's about as safe as it gets.
I was told by a friend not to run my external hard drive from the generator power, even through the Smart UPS - they are very sensitive, and everything on it could vanish on the outside shot that there is a problem.
For those who are curious, here are some other current readings (120 volt power):
4-year old Dell Desktop 2.8 Pentium computer: 0.5 to 0.9 amps
19" flat screen monitor: 0.23 amps
1-year-old dell Desktop 2.3 dual core computer: 0.6 to 0.75 amps (using a powerful computer game). Meter showed 0.9 amps at startup, but this one wasn't sensitive enough to show the peak power surge.
Old Analog CRT TV + VCR + separate DVD player: 0.9 amps
Although it may appear that a 75 watt inverter and a car/deep cell battery would run a lot of this stuff, such as a TV or desktop computer, the initial surge required to turn them on won't let you do so. A more powerful inverter (300 watts), which costs about $40, will probably let you power on these items. Can't say for sure, because I don't have one, but the desktop computer power supply is only 200 watts. If any of you ever get in such a situation, turn on electronic devices one at a time, because of the initial startup power required.
Thank you again for your help -
Alan Darling, KB1ML