Well, sorry if this is a lame answer but until we know more about their personality we're just going to match them up based on ability and gut instinct.
Of course Blackbeard would fight Luffy.
Van Augur would have to go with Usopp, or have some sort of fight with Usopp so we can see who the better marksman is.
I actually think Shiliew would be great for Zoro. He's just so frightening and insanely strong I think it would be someone that's actually a challenge for him.
Even though Laffitte is said to be the navigator, I think he would make for a great fight with Sanji. This is solely based on the fact that I think their personalities would really clash.
This is kind of hard! It's hard to say because when they actually fight I really doubt it's going to be just the Strawhats against them. If they fought right now, of course the Strawhats would lose though. That's the good part though, they have a long way to go before they face one of the final enemies.
Blackbeard pirates would win. Luffy's crew is just too soft. Blackbeard pirates how ever wouldn't hesitate to kill luffy and the strawhats, just like what they did to whitebeard.
Now that blackbeard has whitebeard's devil fruit he seems unbeatable in one piece.
Everybody's saying who'd win, not what your asking so:
Luffy vs. Blackbeard
Usopp vs. Van Augur
Franky vs. Jesus Burgess
Nami vs. Lafitte
Chopper vs. Doc Q
Zoro vs. Shilliew
Sanji vs. Sanjuan wolf
Brook vs. Avalo Pizarro
Robin vs. Vasco shot
Don't know about the last member of the Blackbeard Pirates but I guess Luffy will find a new member.
Are you asking which members would fight each other?
Luffy would obviously fight Blackbeard.
Zoro would probably fight Shiliew since he seems to be the only swordsman.
Nami would fight Laffitte, Blackbeard's navigator.
Usopp would fight Van Augur, the sniper.
Sanji might fight Jesus Burgess because they're both martial artists.
It's impossible to match them all up right now since Blackbeard's crew has more members and most of them didn't show their abilities yet.