I would not recommend a drop ceiling unless you have a lot of height. The drop ceiling will take about 4-6 inches of height, so that you can put the tiles in at an angle and work the tiles around until they fall into the rails. Also, the installation cost for a drop ceiling and dry wall are fairly equal. A drop ceiling will reduce the value of the basement. Drop ceilings are frequently used in home theaters so you can deaden the sound but the acoustic tiles are more expensive. Installing dry wall on a ceiling is bear and it is fairly cheap to have a dry wall contractor install it for you. I would leave some access panels near spots you have to access (e.g., water valves).

For flooring, I would have carpet if that is what you like. Personally, I would use vinyl wood-look planks and use an area rug above it.

If you are going to finish a basement, put some thoughts into the functional elements and not just the finishes. You need to look into heat/cooling the space (I suggest a mini-split system but you may need several for different rooms), hiring a plumber for the bathroom, and installing a lot of can lights in the living space

I would put carpet in but tile the area near the doors.

Carpet is cheap. Don't spend too much and it's not a big deal should you ever need to replace it.

My basement is cold in the winter. As you finish the basement that is something to think about/factor into your decisions. Another reason why carpet is a good choice.

Ceiling tile is horrible, it's easy to cut drywall

Starting to think about finishing the basement. Some friends and contractors have begun making suggestions, and I'm not sure what makes the most sense.
We've been in the house for 5 years, and we've never had water/flooding issues. The back part of the basement has French doors and some windows. We have rough ins for a full bath. We plan to add a bedroom in addition to the bath and a rec room.

RE: ceiling - some folks have suggested a drop ceiling so we can access the pipes if there's an issue down the road. They're ugly but practical I suppose. Thoughts?

RE: flooring - some folks have suggested tile in case we have a flood. I'd prefer a cozy basement with carpet (so the kids can play and I won't have to worry about concussions). And tile in a basement bedroom (even with an area rug) seems like a bad idea. Thoughts?

I'd appreciate tips from folks who have tackled a similar project.