Setting up RRC filter and useful equations
First of all, the correct equation for an RRC pulse is given here.
You are correct that you need to define the sampling frequency Fs and the symbol interval Ts. The number of samples per symbol interval is then Ts*Fs, which I assume to be an integer.
You also need to define beta, and the pulse duration D. For simplicity, let's assume D is given as a multiple of the symbol interval Ts.
Then, you can easily define the time vector. Assuming symmetry around zero:
t = (-D/2)*Ts:1/Fs:(D/2)*Ts;

Then, if you have a function rrc(t) that evaluates the RRC formula for a given time vector t, you're done (all you need to do is transcribe the formula I gave above into Matlab) or whatever language you use).
Note that you don't need to worry about upsampling. The symbols that go into the RRC filter have to be upsampled to space them out by Ts, but the filter itself doesn't have to be.
For more details, see Chapter 11 in the book linked at the bottom of the page here. That book is actually quite practical and may be a good complement to your current textbook.