I have to complete form 1120s and form 1040. The I have to do Virginia form 502 and Virginia form 760. What turbo tax software packages do I need?

To do the 1120S return, You need Turbo Tax Business.
TT Business is for 1120 Corporation, 1120S Corp, 1065 Partnership or 1041 Estate/Trust returns and will not do your personal 1040 return.   It  is a separate program from the Desktop Home & Business program or the Online Self Employed version.

Home & Business (or Self Employed)  is for personal returns that include a schedule C for self employment or sole proprietor. A single owner LLC would be reported on Schedule C unless the LLC elected to be treated as an S corp or C corp.

You will get a schedule K-1 (or a W2) from the business return to manually enter into your personal 1040 return.

Turbo Tax Business  is not available to do online or on a Mac.  You can buy the Window's version here.  And you can have both TT Business and TT Home & Business (or any personal version) installed on  your computer at the same time.
https://turbotax.intuit.com/small-business-taxes

Then you need a personal program for your 1040.  Any Desktop program will work.
Https://turbotax.intuit.com/personal-taxes/cd-download/

If you want to use the Online version you need at least Premier to enter a K-1 from the Business return.