1. Yes, you have to get a debit card from the bank that holds your checking account.
2. Credit or debit refers to two TOTALLY different types of accounts. A debit card allows you to make electronic withdrawls against your checking account -- that is, debits. One thing to note (that's burned some people I know) -- a debit card is basically an electronic checkbook. This means that in some cases you can commit electronic debit transactions that would move your account balance into the negative, which is basically the same as bouncing a check. So you still have to balance the account, and you need to keep up with your balance. Most of the time you will be able to make a $120 purchase on a debit card against a checking account with $100 in it. You'll just get hit with insufficient fund fees and other charges. This can compound into a really bad situation. Be sure to read the bank's fine print and UNDERSTAND it.
In some cases, you have overdraft protection which basically lets you get away with bouncing a debit transaction. The difference between the debit and your balance goes onto a credit card type of account, which is a revolving credit account that will normally carry a pretty stiff interest rate.
A credit card is basically a line of credit. A provider will let you charge up to $X so long as you make minimum payments. They'll also charge various fees and finance charges on your outstanding balance. Living in credit card debit is a bad place, so be careful with these. Interest rates on some cards car get downright ridiculous.
Credit cards can be 'secured' on 'unsecured' -- secured means that you have to put money in a savings account, and that's basically the credit card company's collateral on you. In other words, they will give you $X in credit if and only if you have $X in an account where they can seize it if you don't pay the bill. Generally you get these deals if you're a bad credit risk. Unsecured aren't backed by a cash reserve, so they're more like 'real' lines of credit.
If you're new to this credit/debit thing, then PLEASE don't go nuts and get yourself into a financial hole.
Debit card will come from your bank.
Your bank may also offer a credit card but there are many more options for you to choose from. Depending on your credit, you'll have good or bad options. Good luck.