Well,
As for
grading, I like PSA grading.. personally.. because they grade for situations of the card, not conditions of the card. that's what i think...so, PSA is very good if u wanna grade vintage card or older cards.. (but anyway, now everyone once in a while tries to get their cards graded, so hey, it works)
and PSA gives fair view of rating while BGS gives pretty strict view.. therefore, the latter could possibly remark very rare pristine condition cards and hard to find high grades... (good for company image, bad for hobby collectors to rise up the price unconditionally)..
Durability, I like BGS better.. they seem to construct with better chemical on frame (slab)... and display and banner description is a bit nicer..
Stackability, PSA rules.. BGS is okay, but BCCG u cannot just stack them.. it's waste of space and scratches to the holder.....
Apart from these 3 criteria, the only thing i think is, i want to get at least psa9 or bgs 8.5 grading when buying.. they will usually sell near the book value, sometimes, a little bit above depending on the population (i mean, recent cards, not vintage).. so i could afford them
So, there are several companies (nowadadys, sports stores themselves grade the cards before they sell if the cards would grade high)...... with 4 main ones..
Beckett (has 3 sub gradiing company, BGS, BVG, BCCG)
Professional Sports Authenticator (PSA)
Sportscard Guaranty Corporation (SGC)
&
Global Authentication, Inc (GAI)..
in eBAy.. they said, you can reply on above 4 companies..
and also this one.
Sports Card Direct Authentic SCD
If you wanna buy off from ebay.. i like to buy PSA and BGS..that's my personal choice and i cannot afford to stack many different companies.
if you want to grade the cards in your possession, all you have to do is, what kind of cards u want to grade (i.e. game used, auto, common).. and there are some PSA members here.. (hill33, whereiswally78 and etc...).. just post it in card discussion forum.. i am sure PSA members will help you out here..
Have seen many cards being graded through members here..
hope that helps.