Congratulations on starting your own business.
Invest in a tax software package right away; I can't recommend a specific one but there is enough information out there to point you in the right direction: share with us which one you ended up using and why (maybe a separate question?)
You do need to make your FICA taxes but you can write off the SE part of it.
Keep all your filings as a PDF, a printout and a softcopy in the native format of the tax software package: it really helps the next tax season.
When you begin your business, most of the expenses are going to be straightforward (it was for me) and while I had the option of doing it by hand, I used software to do it myself.
At the beginning, it might actually seem harder to use the tax software package, but it will pay off in the end.
Build relationships with a few tax advisors and attorneys: you will need to buy liability insurance soon if you are in any kind of serious (non hobby) business and accounting for these are no trivial tasks.
If you have not filed yet, I recommend you do this: File an extension, overpay your estimated taxes (you can always collect a refund later) and file your return once you have had a CPA look over it.
Do not skimp on a CPA: it's just the cost of running your business and you don't want to waste your time reading the IRS manuals when you could be growing your own business.
Best of luck and come back to tell us what you did!