Discogs is your best bet to find quality second hand vinyls. Look at the marketplace for each record in that list. Some are dead cheap so you can probably get a decent ML vinyl collection for about £30 I reckon. Of the studio albums Coudln't have said it better is hardest to source, followed by Bat 2 and Welcome to the neighborhood. Bat 2 is useless as it was a single hot vinyl pressing (thus soft and gives you bad quality playback) and is more of a collector's item than a properly playable album. Those 3 albums are now more for the completists I guess.
Bat / Dead Ringer / Braver can be bought new via Amazon / HMV and other places.
No Meat Loaf compilations on vinyl beyond Hits out of Hell as far as I am aware. That one can be bought second hand for sure. Just look for the ratings on Discogs. I usually only buy Mint / Near Mint / VG+ etc. Most sellers on there are good from who I've dealt with. Just look at their feedback.
eBay can perhaps be used to source very rare copies but I wouldn't recommend going via that route initially. Many bad copies on there from my experience and some people load them off on occasion rather than know how to send or handle vinyl properly. I got a Phil Collins double vinyl sent to me and it was wrecked as the guy used binders to protect it. Useless.
A new copy of Bat I think makes an excellent birthday present if he doesn't have it yet. Best place to start I think.