Have you thought about Discover IT or Amazon Store card? You can use the cash back from Discover on Amazon.
The Amazon store card has promos for 0% if you spend over certain thresholds.
For most customer initiated CLIs, you should expect a HP. Amex is the only CCC that's particularly known for their SP clis. For chase, expect a HP unless it's an auto-cli.
Chase will likely give you an auto-CLI after 3-6 months.
Given the limited value and utility of ThankYou points, I'd recommend you apply for the Blue Cash Preferred instead of the Everyday version, and use its 6% cash back at supermarkets to buy Amazon gift cards. Especially if you can get a lot of your textbooks and other school needs on Amazon, you could probably make the most of that. (Also, I think the Forward becomes somewhat more useful once you're 21 because their "entertainment" category includes many bars)
Also, since you're an online shopping maven, don't miss the deals in the Ultimate Rewards Mall. You can really rack up the UR points at many online retailers that way. Some of them will get you as many as 10 or 15 UR points on the dollar. And UR points are way more useful than TY points, if you eventually get the CSP and unlock the ability to transfer them to travel partners.
A good year of gardening is in order for you - 2 is probably too conservative, but with a short file like yours I'd give it a good year of perfect payments on the cards you have. Then I'd app the cards you want, but you may end up needing to do some mid-tier cards before going for the big ones like BCP and CSP. Chase Freedom is more welcoming to short history than CSP. And Amex is more welcoming to higher incomes than student-sized ones. I'm not saying you won't be able to get at least one of the two a year from now, just that it may be a stretch.
If I were prioritizing, I'd make getting the Amex BCP, or any Amex (the BoA one you have doesn't count because it's not issued by Amex, just on their network) my top goal for a year from now. Then, for the rest of your life, any new Amex card will backdate to 2014. I only wish I'd had my first Amex that early in my life.
It's really too soon to speculate in detail on your likelihood of approval. You have a great starting portfolio for someone brand new to credit, so your scores can grow significantly over the next year if you just use the cards regularly and pay them timely every month.
When it gets close to that anniversary, post up your scores and and tradelines with limits and we can give you some idea of your chances.
For now just use the BoA and Freedom cards frequently, and dig the Cap1 out of the sock drawer now and then to keep the account active.
You might also want to get a parent to add you as an authorized user on an older account that has a larger limit.