If it's simple (one account, a few different categories of expenses), I'd stick to Excel, Google Docs or just a ledger. Just set it up like a checkbook register and record any income or expense on a separate row. Don't get too fancy with categories and maybe just start with these expenses: Necessities (rent, food, clothing, utilities), Discretionary (dining out, cable TV, movies), Work-related (software, supplies).
Software isn't going to help stay budgeted or with tracking unless you commit to entering the data. Once you have the raw data inputed, you'll have lots of options now and in the future. You don't need all the fancy reporting features of Quicken.
If I recall, Excel has a ton of templates for just this purpose. There are many free apps for iOS and Android that will help you track your expenses as well; this has the advantage of always being with you so it should be easier to do. Some allow you to take a picture of a receipt to help with documentation or you can use Evernote for that.
I use Quicken 2011 via Virtual Box but I have messy personal finances. I've used Quicken in the past for a small business using cash-based accounting method for more than 15 years. If you have to go with accrual-based then you should consider Quickbooks.