Hard to say... Barclay likes to see history and with no cards from them you might have difficulty.
i just got a Sallie Mae yesterday... After being an Apple card member for 16 months.
I started with Barclay in 9/13 with a $1200 Apple that I used to buy an iPhone. They auto CLI to $2200 at 6 months... then nothing else. I never asked for a CLI because I didn't want a HP. Once you get past the account opening 0% purchase promotion the card has no other rewards and becomes pretty useless. It still helps build credit with Barclay though!
That being said, I achieved my goal after 16 months with the Apple card. I wanted to get in the door with Barclay (which I did with the Apple card) then yesterday I applied and was approved for a $4500 Sallie Mae. I then took the $2200 Apple CL and moved it to Sallie Mae... and closed the Apple.
Mission accomplished.
YMMV but that's how I got my instant Sallie Mae approval... I also gardened all of 2014. I had just a couple INQs across the board and $0 balances reporting on 7 of 9 revolving accounts with UTI less than 30%.
In regards to Discover skipping a month, its normal for them to do so in a month you receive a CLI, it will take 2 statement cycles to update at the CRA, a glitch in Discovers system, it can be useful in certain cases where you need to carry a balance for a month and dont want it reporting.
Welcome to MF 
@Anonymous wrote:My balances are paid in full every month, but if that isn't enough then I don't want to risk a hard pull. If it's too soon for this Sallie Mae card, I might go with an AMEX instead. The Sallie Mae is more appealing though.
The only problem I see is AAoA.
Flip a coin IMHO...
Apply !
I didn't want anymore cards with the exception of the Sallie Mae & know in 2015 that I will NOT be applying for anything....and after the roll of the dice - APPROVED !!!!!!
Not my highest credit line (2500) but 2 years ago they wasn't happy with the strength of my current profile (too many new accounts & inquiries). But I looked back to see what credit bureau they pulled back then (Transunion) & knew that report had no "hard inquiries" at all & it payed off for me ! The delay of doing so in 2014 was that I wanted my accounts to hit the one year mark minimally, with the excepton of the recent US Bank Cash Rewards card. I am not sure if they pulled the same because if they pulled Experian, I would PROBABLY not be sharing this joyful moment 
@Anonymous wrote:I actually think you have a very strong chance at approval, if not instantly, then at least upon recon. Barclays actually seems to prefer if you only have a couple of cards. It seems like their ideal number of credit lines at time of application is 2-3 (enough to show history, but not too much to appear credit-hungry). The Barclays CSR I talked to more or less said as much when I reconned to get the Sallie Mae card. Obviously there are people who are approved more and people who are approved with less. But that really does seem to be the trend. My brother, who only had one previous credit card, was just approved for a Sallie Mae WMC with a $4700 limit (random, I know, but rather high for a starting limit on that card).
Good points.
For me it was all about getting in the door with Barclay in 9/13 when I got the Apple card. The Sallie Mae was the card I wanted all along... But didn't bother with the app given my scores at the time.
Here we are 16 months later and I have a $6700 SM after the approval and transfer of my Apple limit. I got what I wanted... Just took a while.