I would definitely recommend a calculator, I’m quite found of the ti-84 and 89s. You could get away with any of those three calculators for engineering. A TI-84 calculator is around $90, a much better use of money than buying two pairs of jeans or a couple dinners out. I’ve had my ti-84 for almost 7 years, so at $13 a year is a steal. Personally, having a calculator in general is super useful for engineering and non-engineering classes. My vote would be for a ti-84 because it has lots of functionality, but not so much that you become reliant on it to solve/simplify problems.
As far as the theoretical and practical engineering go with numbers vs variables, you’re going to want a good mix of both. I can’t imagine doing entirely one way or the other for four years. I would assume a good engineer should be comfortable with both methods.
Protip: Even if you work entirely with variables, assigning arbitrary values to variables can show that you correctly did your equalities or derivations.