Congratulations on your first job!
I use CommitCRM (
www.commitcrm.com) which almost everybody would agree is like the number one software since it is made specifically for the computer industry. It can keep track of a lot of various information about ur customers, even their assets, etc. Many great features, sign up for a free trial if you would like. The only downside might be the cost of it some would probably agree, but it pays for itself.
As for accounting, while you can create and track tickets in this system, it does not keep track so much accounting stuff, for that I use Quickbooks because its also able to integrate very nicely with CommitCRM.
An alternative solution would be Microsoft Accounting Express 2008 which you can download for free or purchase the "Professional" version.
I hope this helps,
James