You're looking up toward the monitor and down for close distance reading. The best combination I've found is mid-range for the main part of the lens and a small bifocal or progressive part at the bottom for reading.
For strictly reading get a pair of grocery store reading glasses, no need to pay an optometrist for that. Actually you might get by with a lower diopter correction from the grocery store for computer use as well, but then you need to keep changing glasses for reading.
And one last comment. If you ever think you have a problem with your eyes, go straight to an ophthalmologist. Don't waste any time on an optometrist; eye problems can develop and become serious in just a few days.