This is the place to ask questions about Cattleyas, even if they are beginner questions.
Slc stands for Sophrolaeliocattleya. It's a hybrid of Sophronitis, Laelia and Cattleya species, though I believe all of these have been recently reclassified as just Cattleyas. At least, I think that's what I read.
Lc is Laelia x Cattleya
Blc is Brassovola x Laelia x Cattleya.
This Slc hybrid is a miniature. I saw this one at Seattle Orchid when I was there and the plant seemed a tad fussy, so I passed on it.
If you really want a good beginner cattleya and want to try a species, look for Cattleya Walkeriana.
I've had my eye on Cattleyas for a long time and have been told repeatedly that Cattleya Walkeriana is great for newbies. It stays under about 6 inches tall and is fairly tolerant of inconsistent care. Mine so far has been the only "set it and forget it" sort of orchid I have that doesn't live in a glass box with carefully monitored temp and humidity. I give it good light, I water it when it's dry and it grows stuff. You really can't beat that for low maintenance.
It also puts on a good show when it blooms.
C. Walkeriana has a pinkish purple flower, but there is also an alba variety that is pure white and a semi-alba that has a purplish pinkish colored lip.