One of the fundamental rules of photography is that the best images are always on the film that was damaged in processing.
How are you agitating your film during processing? In my experience, agitation is the key to good processing of film. I presume you are using a small tank with inversion agitation. For development, I use continuous agitation for 30 seconds, followed by 5 seconds out of every thirty seconds for the rest of the development time. And agitation means completely inverting the tank, flipping it from one end to the other about once every second with a sharp twist of the wrist, followed by a gentle "wiggle" at the end of each agitation cycle to dislodge any bubbles that might have formed on the film.
For fixing, I believe in continuous agitation throughout the fixing cycle. With fresh rapid fix, I find that 3 minutes is adequate. Be careful of overfixing with rapid fix - that can bleach out highlights in the image.
You mentioned two specific symptoms - 'underfixing' and "thin negatives'. How do you know your negatives were underfixed? There are two visible symptoms of underfixing - if they are cloudy, then they are grossly underfixed. Note that sometimes underfixing isn't apparent until the film has dried, and shows us as uneven brownish clouds. Just refix and rewash to solve that problem. By the way, be careful when you evaluate your dried negatives - if you hold them up to a bright light, the area immediately in front of the light might look "warmer" than the rest of the negative leading to an incorrect belief that they are underfixed. The best way to evaluate negatives is to either use a light box, or to look through them toward an evenly illuminated white wall.
Another symptom is a uniform pinkish color. This is especially the case with t-grain films (Kodak T-Max, Ilford Delta). Again, refix and rewash, and the problem will be solved.
In either case, however, you should be able to completely fix film in three minutes. If that is not happening, then the most likely causes are insufficient agitation, or excessively diluted and/or exhausted fixer.
And always use a stop bath. For film processing, the stop can be plain water. The essential function of a stop bath in film processing is to prevent carrying developer over into the fixer. A brief (30 seconds) plain water stop bath will make your fixer last a lot longer.
On your thin negatives, were the edge markings distinct, or were they also thin. If the edge markings were also thin, then you underdeveloped the film - either because of incorrect developer dilution, exhausted developer, or insufficient agitation. If the edge markings were distinct but the image area was thin, then the problem was most likely underexposure.
Final thought - when you are first starting out, the best thing to do is to follow the manufacturer's instructions exactly and ABSOLUTELY CONSISTENTLY. Once you find that you are getting consistent satisfactory results, you can then think about fine tuning the process.
And always remember that the images that you saw will be better than the images that you captured on film.