Bill;
A lot will depend on your Generator. I don't remember what you have. If it is like a lot of them, not ic regulated, I would recommend having it surge protected. Many will vary quite a bit in output voltage when a new load (microwave, A/C) kicks in. A good surge protector will give you that protection and also set up a delay of approximately 2 minutes before it will restore power. Inverters are another story. Some are modified sine wave and some are full sine wave. I won't run my computer on a modified sine wave inverter. They don't like it. Some higher quality stereo equipment, the same thing. My cheap stuff, no problem. I have a little Honda 2000 that serves me well with no surge protector, but it doesn't run the A/C or Heat Pump either. Just my 2 cents.
John