I'm new to Half-Life Series

Half-Life: Source is the basic HL1 with source engine, but if you want a REAL source engine go with Black Mesa!

HL: Source is just the original ported to Source engine. There are very few graphical changes, though.

As for the order: HL1 -> Opposing Force -> Blue Shift -> HL2 -> HL2 Ep. 1 -> HL2 Ep.2. I think Lost Coast isn't canon, but it would fit after Ep 2.

If you want to play in chronological order, you could simply google the right order or check wikipedia. In any case you just start at the first game, Half-Life.

start iwth number 1, end with number 2 e 2

If you feel you can enjoy a game so old like the first Half-Life play it, it's a masterpiece. You can easily skip Opposing Force and Blue Shift if you prefer, but they aren't bad. Don't think you should consider Black Mesa instead of the original, but maybe after playing the classic you could try it.
After the first one, go with Half-Life 2 and then the two episodes.

Fuck that HL1:Source - get real with the original HL1!
Kids these days... don't appreciate the classics as they are...

Hey since you have the half-life games I suggest you check out the Sven Co-Op mod. It basically half-life with friends and it's so much fun. Some servers do the Half-Life storyline from start to finish, but rarely. Seriously so much fun