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I would definitely wait awhile and try to pay off the collections as soon as you can and get the AAoA well over a year. Your scores will go up eventually, but it will take patience. As far as Chase cards for the 700+ club, I was fortunate two years ago to get approved for both the Freedom Unlimited and Slate cards back to back with a 625 score directly through the bank. I was even preapproved for the CSP surprisingly during that time but didn't pull the trigger (thank god). You may have a better chance getting approved with a Cap1 card if you give it about six months or so after you pay off most of the debts.
Don't waste the hard inquiry. I would wait a year or two and build up my credit score with the cards at hand. At this point, like everyone else is saying, you have a 0% chance at getting a card issued by chase. They abhor collections on an account. Most, if not all get insta denied and I've even heard some get the same treatment way past paying it off, Somthing like 4-5 years. Chase is very picky like that. Stick with capital one or discover until the collections fall off your records.