my .02
you should snag that CSP.
If you do anything else just make sure you hit that CSP button first.
I agree with having a plan to which buttons you hit and in what order if you do a spree.
I laid mine out and hit them in the order I wanted them and in the order I knew the hardest ones would get looked at first.
I had reasonable success. Can't really complain.
you're scores look like you could withstand a spree/attack on at least 4 banks and should be able to walk away with at least 4 cards and $40k in new credit.
but that's just at a glance without knowing anything about your income or profile.
@jesseh wrote:
Chase gives me the following prequal page:
(my name above it)
(
So, does the fact that it shows a CSP, mean I can be sure to get a 5k limit?
I would suggest taking only the Freedom for now. This will give you a start with Chase, you can start earning UR points on a no-AF card, using the quarterly categories that they have on the card in 2016. Using the Freedom will give you a track record directly with Chase, and then later you can decide whether you want the CSP or not.
What is the specific Prequalification you get from Capital One?
I would suggest getting a Capital One Quicksilver, no AF card. This will get you started with Capital One. Later, after you have a track record with Capital One, keeping the Quicksilver active, you can app for the Venture card, and will likely get a much larger CL than any other CCC would give you at that time. The Venture has a spend bonus which you can use to get some travel points. Then, after 6 months if you decide you don't want the annual fee, the Venture limit can be moved into the Quicksilver limit.
Using these two cards, since you are early in your snail growth phase, is a good way to keep your journey real. Can you get 5 cards right now? Probably. Is that the best choice for someone just starting out? In my opinion, not at all. not at all. Take some time to work with basic cards like Freedom and Quicksilver, then look at what else is available, ask a lot of questions, and take your time.
Good luck!
p.s. Since your scores are in the mid-700's, you don't need to include "no baddies" in your siggy. The scores say "no baddies" already 
@Creditaddict wrote:
It's common knowledge to get 2 chase cards and 2 cap1 cards with same pre-qual and same hard pulls... Why would you suggest not only just 1 of each of these cards but 1 of each of the lower tier cards known not to issue the higher limits??!! That's BONKERS!
If you are going to take 1 of each (crazy) but if you are take the premium and higher limit giving cards (venture, and csp)
Because not every one can handle 7 cards in their wallet when they are just starting out on their credit journey Or the bonus spend requirements of $7,000 in 90 days to thoroughly earn the CSP and Venture bonus. Heck, many of us with lots of cards and expenses can't even fathom that level of spend. Someone with currently low value cards, I'm almost certain canNOT in any visualization get $7k of spend done in 3 months.
By the time OP gets an understanding of the next phases of this journey, meaning deciding whether CSP makes sense, whether Venture is necessary, these HP will be a distant memory.
Besides, OP's original question is "Spree or snail" Not What is my best spree strategy?