Personally, I wouldn't apply if I wasn't pretty sure that I'd get approved. Those hard inquiries add up and some institutions will shy away after you have so many. But if you're just going to wait for a year or two to apply for Chase cards and not do anything with your credit in that time, then you may want to roll the dice and apply sooner than later to find out.
Chase is a good place to start, but keep in mind what others have said about credit history and banking relationship - it may be ideal to get a checking acct with Chase for now while your history builds up. I'd look at Chase's 5/24 cards and see which ones you want. If you apply within 24 months of when you got the Discover It, you are at 1/24. If you want to get four 5/24 Chase cards, you shouldn't apply for anything before that. But if you only want 2, then you can apply for 2 more cards with other institutions in the meantime. Of course it'll take a bit longer for your account history to age.
That said, my second card was a Freedom back in 2011, although my first card (with Wells Fargo) had been open for 5 years - but 4 years later I got a slate, then 2 years later I got a freedom unlimited, ink preferred, and sapphire preferred - then was denied for the Amazon card for too many recent requests for credit (applied same day as csp). I also PCed the slate into a second Freedom. The point is I think having an older Chase card not only helps you build history with them but also gets you approved for more cards ultimately since you're not doing a bunch at once. Maybe see if you can become an AU on an established Chase CC account?
Things to consider...
