Paying off derogatory items will not improve your score. The damage is done and will remain for the balance of the 7 year reporting period. Mortgage companies will require that all derogatory items are settled before approving a loan.
It is really bad advice to tell you to dispute legitimate negative items. They are not likely to be removed and even if they do fall thru the cracks, it is highly likely that they will return when the creditor next updates. Mortgage companies pull your credit report several times, including right before closing.
Paying off current, open credit card balances can give your score a quick boost, if you have been carrying balances of more than 30% of your limit. Paying off the cards will also improve your debt to income ratio, an important factor in the loan approval process.
It may be a real stretch to pull your score up to 620. You should keep in mind that even if you get to the 620 point, that doesn't mean you will be approved. There are many other things more important than your score: your entire credit report, stable work history, salary, debt to income ratio, other assets, downpayment and closing.
You will need at least 24 months of consistent, on time payment history to improve your score. You may have to wait on that house.