I'm not sure if these are the 'best' paints for greys and reds, but I use mostly Wargames Foundry
paints. The actual colors of the coats could vary wildly depending on many factors so most shades would be fine.
I normally paint in triads (three layers - not sure how familiar you are with painting minis) For Greys I've used...
Slate Grey (32A-C)
Slate Grey (32C) and Arctic White (33A and B)
British Gun Grey (108A-C)
Bright Red (15A-C)
British Redcoat (68A-C)
I find Foundry gives pretty good coverage with a single coat of the 'A' color with maybe a quick touch up here and there. I think there are some Games Workshop paints mixed in as well, but I don't recall the actual colors. The GW Base paints
are amazing for smooth colors in one coat, even painting yellow over black for instance.
You can find all of my units in the 1690
page of my blog. If you hunt around older posts with the BLB tag
on the blog, some of them have the specific paints I used. I think there are some Games Workshop paints mixed in as well, but I don't recall the actual colors...
This post from the LoA blog
is also worth a quick read.
Hope that helps!