Welcome to the forum.
I see a number of 70 - 300 lenses out there. Should these be sufficient??
These are usually the 'entry' or 'beginner' level lenses, and as such, the are designed to be cheap rather than optically great. But they can still get good results in the right circumstances.
The main problem with them is that the max aperture is rather small. When you are zoomed out to 300mm, the max aperture is only F5.6, which might make it hard to get shutter speeds fast enough to keep the images sharp. In bright light, it should work fine, but shooting at dawn or dusk may be very challenging unless you are shooting landscapes and using a tripod.
Also, these lenses are typically a lot worse at 300mm than they are at say, 250mm...probably due to the cheap design.
If you can afford it, I'd recommend the 70-300 VR over the ones without VR. It will certainly help get sharper shots when the light is failing, as long as your subjects aren't moving too much.
Don't be afraid to crank up the ISO if you can't get your shutter speeds high enough for sharp shots. This will introduce noise into the images, but noise is often better than blurry shots.