It might cost more money, but you can use the banks own system to order checks. That way you know they have the right routing and account numbers. When you buy a box of checks they will generally have an order form in the box, that will guide you through the process. But you don't have one because this is your first order, or you lost the paper a long time ago. Still use the banks website to order the checks, it is worth the extra few bucks.
The check number is not a big deal. Some people want to avoid low numbers because it looks like they have a new account. In fact I have seen some merchants reject low number checks. They might call them starter checks. They are afraid of fraud. (I have no comment on the logic or appropriateness of their concern, I am only noting that I have seen the signs).
Just guess high. Don't worry if the first few checks started with 001 or 101, so start with 1001. You don't even have to use the bundles of checks in the right order, the bank software won't reject them. Some couples each have a bundle of checks, and write them against the same account. The bank might get concerned if the same number appeared close together, but if they were years apart they won't even notice.
Some banks use singles and some use duplicates:
Duplicates have a carbon sheet under each check. When you buy something at the store you fill out the info (store name, amount in number, amount in words, date, signature). You then tear out the top copy. The carbon left behind has all the important info (what you wrote and check number). When you go home you can then update whatever manual or electronic system to use for tracking your money.You can also use the register part of the checkbook to record this info. For safety the carbons don't include all the bank info, that way if you lose the carbon, somebody can't get all the banking info.
Singles: There is no carbon copy. Some have a stub on the top or the side that you can jot down the vital info. You can also use the register part of the checkbook to record this info.
Both types of checks are used to spend your money. You give them to stores or people, or send them in the mail. They then deposit them in their bank account.