I've basically done all options!
For DD1, we had a Mamas and Papas chest of drawers with a removable bit on top to make a changing table. Was useful to start with, but then I didn't like using it sideways as pp have said. And once DD1 got too wriggly, it felt safer to change her low down. It has been a nice set of drawers to keep without the changing bit on top.
For DD2, we just had two caddies and two changing mats - one upstairs and one downstairs. I changed DD2 on either the bed or the floor. Much easier with a toddler wreaking havoc in the background.
When we go and stay at DMs, she has a wooden changing table thing that sits on top of the cot. I find this the most annoying option as im constantly putting it on, taking it off for naps, putting back on for nappy change etc. Also, because it's straight on, you are right in the firing line. During a nasty bout of noro whilst we were staying with DM, DH got projectile diarrhoea all over him as a result of the angle of exit from DD1 😅🙈 I've gone back to caddy + changing mat at hers.
In any case, as baby will be in with you for the first six months, you won't want to be going into baby's room to do a nappy change during a feed or whatever, if you've been feeding them in your room. So save yourself some space in the baby's room and just get something basic set up in your room to start with.