Credit Score Management

I have three unpaid medical bills from four years ago on my account. I was going to pay it off (I can afford to now) but I’ve hread it will lower my score and make it more recent. I also have student loans of 50,000. I just paid down my two credit cards to 10 % of my available credit. I’m going to wait until October to apply for a home loan. I am hoping my credit cards pay off will make my score rise by then.

Here’s the background info:
Came to the US in mid-2001, opened my first credit account shortly thereafter.
Everything was going fantastic, making ontime payments, keeping my balance low, until mid-2004 when I hit a bump on the road, which resulted in several late payments on several accounts, a couple as late as 60, 90 days.
Picked myself up a bit, but have been only able to make minimum payments. Cards are maxed out, which is the reason for my score of 580, I guess.
Have about 4K in credit card debt, which I am plotting to pay down completely within the next 3 months.
How much and how quick can I expect my score to increase? When will it reach a respectable level assuming everything goes well from now on?
Thanks in advance.

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