Hi Nortilus,
The red star near Beta Crucis is now known as DY Crucis (a fairly recent designation which acknowledges that it is a variable). It has a general magnitude of 8.9 and is one of the reddest stars we can easily see.
Also known by an older catalogue listing as Espin-Birmingham 365, it has a popular nickname, at least here in Australia, of "Ruby Crucis".
If you'd like to hunt down other red stars, here's a listing of some of them, prepared by US astronomer Brian Skiff.
ftp://ftp.lowell.edu/pub/bas/starcats/bsa.red
Coloured stars are great fun to observe!