Absolutely is not worth it. I used to have chase checking until a few months ago, but I remember the latest update they sent out was that it was 4 dollars spent gave you one point of cash back. Which basically amounts to 0.25% cash-back (if even). Granted, it is free as long as you make 6 transactions or receive a direct deposit. If you absolutely want to stick to debit, check out PerkStreet: PerkStreet Financial
They normally have 2% cashback on all purchases and they have a special promotion of 5% for the holiday-- this is better than almost every single credit card out there! However, perkstreet is pretty new and I am not sure how long they will be able to last with such a good deal, if you want a more trusted source, INGDirect has been around for a long time (and is definitely here to stay, ING is one of the largest banks in the world) and has some cash-back incentives, besides being totally free checking without any gimmicks (like Chase).
for travel, I do not
recommend using debit cards. If they are lost/stolen, that money is gone from your account. Yes, you will get it back, but in the mean time, you will not have any money in your account. I'd definitely follow the suggested route and get a secured card. I am willing to venture in as little as 6 months with responsible use, you would then be able to qualify for a normal card, albeit at a higher interest rate.