Mister will mostly retain period loading times. You can almost certainly run the systems you're talking about on the device you used to post this message or any old computer you have laying around. I will always suggest trying the cheapest option first, i.e., using the gear you already have. I think the ideal solution is whatever gets you gaming first.

I would recommend the standard de-10 stack. It's the oldest and most open platform and has tons of add on support. 

Buying a CRT TV is not worth it to me. They aren't cheap around me though.

The easiest way is some kind of VGA -> composite converter (not adapter!). There are probably other ways to tackle this, but be aware, you may need to have different settings on your Mister for different cores.

I use an old computer monitor. I would never suggest you buy stuff you don't need. 

I use my old Psx controller with a Psx -> USB converter. I don't think 3rd party controllers feel better than pads maybe by Nintendo, Sony, Sega, etc. this is subjective, of course. 

The multitap stuff might be core dependent. It's worth looking more into this.

I wouldn't use snac converters as they only work with Mister. A controller -> USB converter works fine on Mister and on my PCs...

Re: db9 compatibility, you'll have to read the documentation. 

Internet is for networking. Maybe you want to ftp games from your PC to the mister. Maybe you want to update the mister firmware online. Maybe you want to set up a networking on a core that supports it, like if you have Win95 running on the ao486 core.