Can I use the basic TTax to file both annuity $ received and a very small self employed income?

With the CD/download product installed on your computer, you can use any version since they all have all forms. 

With the online product, you must use Deluxe or higher to enter Self Employment income because it requires a Schedule C which is not in the Free Edition. If you have any expenses that resulted from your self employment income, you need the Self Employed version to enter those.