Creditors "The computer" are basing their CL decisions off previous CL from other cards on your credit profile. If you have no previous cards then expect a low limit.
What I would do if I had a 800+ score? TBH I'll do this with a 720+ score!
First Card.
I would go for the AMEX Blue or Everday card. Why?
The starting limit may be low but AMEX does soft pull CLI up to 3x the original CL after 61 days and then again every 181 days. It's important that you don't request CLI early. Wait the days, truest me. 1k turns into 3k in 61 days then 9k in 181 days then 27k in 181 more days. Some peeople have gon further than 65k. Don't go to high because AMEX will do income verification.
Next Card
I would go for Discover IT, Why?
For the same reason as AMEX except you can keep requesting a CLI ever 61 days instead of 181. You can go nuts and just keep requesting with no harm to your account or score. There's no 3x CLI, some months your increase can be $400 others can be $4500, some can be denied and then you'll just request a increase again after 61 days. Some people, actually a lot of people say they request a increase after each month. I've read some pretty high CL over 30K from users doing this method.
AMEX and Discover are two banks that don't require a HP for CLI and are really generous with their CL.
If you want but don't need to if you get the Discover and AMEX but:
Apply for premier cards that require annual fee "they seem to start CL with at least 5k" then switch the card into an annual free card while keeping the limit. I've done this before with Chase.
What you absolutely don't want to do.
Don't apply for multiple cards until your CL is high. You don't want 10 cards all with 1 and 3k limits!
Wait about 6 months to a year after the high CL has posted to your CP before apping. This will show history with a high CL.
What I would do after that process is complete?
Now I may start apping, I'll probably start at the CU before the Bank because they tend to be more generous. Capital One has been known to be generous as well. There are times where you'll already have a 17K card and receive a 3K CL to start on a new card (Probably a Bank). Those times will blow and you'll feel like you wasted a HP. If I go for a bank let's say a Chase then I'm only applying for the premier cards then switching them to their regular cards (after I collect the bonus).
You're in a good position, great income, no debt with a high score. You just have to groom your CL limits up. Goodluck 
@Anonymous wrote:What's up everyone,
Just to vent and share my experience with you guys. I have chase slate with 1000$ limit for 4 years so far and chase never offer any credit limit increase at all. Last year I decided wether to request limit and take hard pull or open new card and I opted for option 2. So I open new card with Wells Fargo and again my CL was 1000$. Yesterday marked the 12 month with WF so today I called and requested an increase. They say it has to be a HP. I said no thanks
I am really getting frustrated with those people as my credit score is near 800 across all CB and no bad stuff on my report at all so why they never offer increase. so now am stuck with 2 cards with low limits that are not enough to do anything. Like last month I could pay for a plane ticket due to low limit.
Should I: A. put a request with a hard pull with either chase or WF or
B. Open a third credit card and hope they treat me with better limit.
Please advise:
1. What is last statement balance on each of the cards?
2. Are there any installment loans, open or closed?
3. Any other accounts of any kind?
4. What score are you referring to? FICO 8?
@Anonymous wrote:That's what make me wonder why am getting low limit. I honestly don't know why. The only thing I could think of is that my credit history is short (4 years old) but I had the impression that 4 years old credit file is in the ok department. My income is ok around 70000$ and no late payment no collection etc Am also try to keep my monthly spend less than 30% of my limit
1. The age is fine.
2. The income is fine.
3. Keeping your spend down does not help you get a credit limit increase. As far as CLI's go it's better to spend a lot and keep paying it down before statement cuts. The only thing that will affect your score is the balance on the statement usually.
@Anonymous wrote:Really? Is it true that hp for a cli will not affect my AAOA?
It doesn't affect AAOA but a recent hard inquiry does affect your score. I think you're right not to waste a HP on a CLI request.
If your FICO 8's are 800 I think you can get out of 'small limit hell' easily: apply for the Capital One Venture card, or an NFCU card, each of which is more generous than most lenders on starting limits. The downside to Cap One is that it usually pulls 2 or 3 bureaus, not just one.