Thecreditcheck when you first open the cards can effect your score a few points but it rebounds pretty quickly/easily. I have 6creditcards, plan on opening about 5-10 more in the next year just for sign up bonuses to create "free vacations" and maximize cash back potential. Mycreditscore is 817 currently. As long as you aren't maxing all yourcreditcards every month (even if you pay them all off) you should be fine in my experience. Availablecreditdoesn't effect anything from what I've seen personally, as long as you aren't actually highly utilizing saidcredit(getting close to maxing out your availablecreditlimits each statement period).
The truth is it all depends. It's a very "your mileage may vary" kind of thing.
You can use sites likeCompare Best:CreditCards | Car Insurance | CD Rates | Savings | Brokerages | Mortgages
to compare cards. Also, there are ways to get deals for cards that theoretically are no longer available.
For instance I just got the old version of the Amex Blue Cash card. It's 5% cash back at US supermarkets, gas stations, and select drug stores (CVS, etc). 1.5% cash back everywhere else. The card is technically no longer available.
Also, check the fine print on that card Deathwing. Make sure that isn't an introductory "only good the first 6 months" or "up to $1000 per quarter" kind of offer on that BJs card.