Welcome to the board!
First, general advice, if at all possible, do not carry balances on credit cards. Use the card for the rewards, then pay it off. The exception would be deliberate use of a 0% (or very low interest if not zero) rate for major purchases.
Specific advice to your question: There are many cards with 0% balance transfer rates for an initial period of months. Citi has at least two, Discover has at least one, Navy Federal has at least one, etc. I would suggest looking at cards with 15+ months of 0% interest on balance transfers, and within that group, look for a card that you would like to keep in the long run. For instance, you may like the idea of 2% cash back on all purchases, in which case, the Citi Double Cash could be a great option. Or, if you anticipate carrying balances in the future or at least are worried you may need to at some point, you may prefer a "rate advantage" type card with a minimum permanent rate, such as the Navy Federal Platinum.
Low interest rates are a nice safety net, but in general, card interest rates should not matter because you only pay interest if you carry a balance, and we don't want to carry balances (other than special cases as mentioned previously).
I would consider closing any cards you no longer use, unless they have large credit limits so closing them would significantly affect your utilization rate. I would especially think about closing anything with an annual fee that you do not think you need anymore.
As for the Apple Card, sounds like it may be a good fit for you, but the balance transfer card may be more timely, so I might do the balance transfer card first. The nice thing about the Apple Card is that you can apply for it and get a specific offer, with credit limit and APR, with a soft pull. You can accept it or ignore it and try again later. So, there's no harm in applying for the Apple Card. I personally do not find it very useful, but sounds like you might.
JMO. Good luck!
Hi and welcome to the forums!
Have you requested limit increases and/or apr resuctions on those cards?
@Anonymous wrote:They will not adjust the apr so requesting limits on cards I don't want didn't seem to make sense if I plan to transfer balances and potentially close right?
Gotcha. I wasn't totally clear after reading your original post as to whether you had an interest in keeping the cards as the only one mentioned by name was Chase and I figured that could be a keeper if you could grow it.... and KJ had already covered every other point in their post so...
I would be reluctant to close a Chase card ... despite the scores and some decent cards you see in my signature, I can't get anything from Chase, because I am far over 5/24, meaning, more than five new accounts in the past two years. So, just be aware if you close it, you will need to do one of these things: a) get another Chase card before opening five cards in the past 24 months, b) wait until you are below 5/24 again to get another Chase card, c) do without a Chase card.
Without knowing the details of what you have or where your spend is focused, I would:
1 - Check Chase prequalification
2 - Check Discover prequalification
3 - Check Amex prequalification
* In all cases, check on that company's site; disregard "prequalification" on sites such as Credit Karma and Experian, they are not reliable
4 - Check Apple Card offer
That should give you a lot of information for next steps. If prequalified, do not rush to apply, take time to consider which fits your needs the best.
I wouldn't close any cards for now, but as you start getting better cards, I would feel free to close old cards I do not value. Closing a card doesn't lose account age for 10 years and generally won't hurt credit much if at all. To be precise, it would only hurt your credit if it caused your utilization to go over the next threshold (say, from 25% to 32%) or if you went below three open cards and lost the small bonus you get for having three open cards.
Edited to add, opening new cards probably will drop your score temporarily, because it will reduce account ages.
You do not need every card to have a low interest rate, because ultimately, you never want to leave a balance on a card long enough to need to pay interest. It is wise to have at least one or two cards with low interest rates in case of emergency, but it's also fine to leave some that you keep for other reasons, eg rewards/cash back.
JMO 
There is no problem I am aware of with opening another Chase card. I am not a Chase expert, for obvious reasons, but I think you could even open another Freedom if you wanted. Then later, close the one you already have perhaps. Or, you could open a complementary Chase card, keep the Freedom, and seek a credit limit increase on it. Even if not successful initially, there is longterm potential.
Similar thought process with Discover. You can apply for a credit limit increase on a Discover card that is soft pull only. On the Discover site, it's under the Card Services tab. But, it's also ok/normal to have more than one Discover card open at any given time.
Most prequalifications won't show the credit limit. Apple is one of the few to do that. But, any firm prequalification should show an interest rate. When you see an interest rate range, that is often a sign that a prequalification is not firm.
@Anonymous wrote:When I had no credit, had no idea what I was doing and didn't realize why retail cards were so exploitative, I got a few... along with cards that would approve someone just starting out. Now, I'm at a place where I have a bunch of small balances on cards with really small maximums but high interest rates. For instance, I have a Chase Freedom but...$1k max and a 22.9% APR. Do I just apply for a new Chase card?
No derogatory marks, missed payments etc. -- My utilization is under 30%. I haven't applied for anything in awhile. I was looking at Apple's card only because of how often I use Apple Pay.
Basically, what should I go for? Large max, low balance transfer...
Please list your 3 Fico scores, AAoA, hard pulls on each bureau, how many cards do you have, there limits, etc. With these we can give better advice or at least more pointed advice.
A good option to consolidate your ccs debt is a balance transfer to a new cc . Credit Unions are awesome for this purpose. Also general income might help advice if you dont mind sharing. Welcome to the Forum