The answer depends on your level of experience, which I don't know. What format are you using? 35mm tri-x (400) has a completely different tonal range than medium/large format tri-x (320). I'd recommend that your "normal" film and normal paper be from one of the major players, so that you can buy it when you need it.
The important thing is to pick a film/developer/paper combination that work well together. providing good range of tones that you find pleasing.
If you are critically picking a film/paper for the first time, i.e., seeing how combinations actually compare in a finished print, pick 2 very different films, e.g., Tri-x and HP5. Pick two very different papers, such as Ilford Mutigrade and Bergger VCCB.
Shoot a roll of each film, develop in D76 1:1 (a great all around developer) and print both films on both papers. This should give you an idea as to the tonal range you find most appealing in your end product.
Take this combination of film/paper and work with it for a while (at least 6 months). after you've established your baseline, occasional experimentation with other combinations will be more meaningful.
For what its worth, I've fairly much standardized on tri-x professional (320) developed in pyrocat HD and printed on Bergger VCCB. I also like Ilford Warm Tone multicontrast paper. When contact printing I use the same film/developer and print on AZO.