Get yourself an AMEX green card. With a 725, some history, and no dings on your report it should be fairly easy to get.
Since the Green Card is a charge card (and not 'credit') you have to pay it off every month down to a $0 balance (AMEX does have exceptions now but NEVER take them). Since you have to pay it off every month you'll only use it like you would a debit card - i.e. only putting money you can afford to spend on it.
That should keep you disciplined and allow you to have balances and pay offs posted to your tradeline. Contrary to popular belief having nothing at all is bad for you. You might see your credit score go up but you'll never be approved for high limits because you haven't demonstrated your ability to pay off and be responsible with even the lower ones. Higher limits also allows you to get larger loans (mortgage, cars, credit) easier. When credit and lenidng companies look at your report they want to come away thinking - this person is responsible, has paid stuff off, and will pay off our stuff. My wife's credit score is just under 850. But she has very little activity on her credit report so gets approved for $5k - $10k limits even with our combined income. I fluctuate between 720 and 780 and very rarely get approved for anything under $20k on the first shot. And easily getting it tripled after a recon call or 3 months. I put $20k on my Platinum card for a big house remodel without even using the Amex Platinum tool or calling the number for prior approval. I bet I could have gone way higher than that.
Also contrary to what some nikkas in here might say, chasing a high credit limit is not a bad thing if you're disciplined. 1. It demonstrates that you're responsible and trust worthy 2. sure they want to entice you into spending, but it doesn't mean you have to. 3) If the world is ending and you're going to die if you don't get something that costs $35,000...you can confidently know you're going to get that $35,000.
This will also allow you to build a relationship with American Express. I've started traveling again and I don't know what I would do without the Centurion Lounge. I plan my layovers around it.
If you're not discplined and you drop 3k on the card in a month and only have 1k when AMEX comes calling at the end of the month.........then do nothing like everyone else in here said.