Which speed will provide me with the widest compatibility with home DVD players? 4x or 16x? Or does it not make a difference? Thanks.

I use 8X for important projects since 16X makes little difference in overall speed (due to waste at the beginning and end). I have never experienced any problems either way, and reckon the speed is more likely to have long-term impacts, where it pays off to have clean pits and lands.

What about bitrate? What is a safe bitrate to burn my DVDs on for the widest compatibility?

That really depends on the unit, but lower is safer. I experienced problems before when I tried to hit to MPEG-2 ceiling of 9800kbps.

Safest bitrate is a total muxed ceiling rate below 9 Mbps. If you're doing a CBR encode, you should err toward the higher side (depending on how much material you have, of course). If you're using VBR, the average rate can probably be considerably lower, with the ceiling rate set at a higher number. There are many factors to consider, but those are the rules of thumb. Remember to leave room in your rate for your audio (which should always be compressed to AC3 for maximum capability and efficiency).