Treat it the same as any other 35 mm. film: Using readily available film, properly exposed, correctly developed and carefully printed on a good enlarger, you should be able to blow a negative up to 11x14 in. with little trouble. An 8x10 in. print should be no trouble and if you take the time to do the job well, you might be able to get a 16x20 in. print.
If you are extra careful, if you use fine-grained film and if you work with due diligence it is possible to make even larger prints from a 35 mm. negative but, for the average hobbyist, 11x14 in. is about the practical limit. As always, your mileage may vary. This does assume that you are making full-frame images and not cropping in or doing extreme blow-ups.
While it is not possible to say that film's resolution can be measured in megapixels, you can say that there is a rough parallel between film grain and digital pixels. Just as you say, if you blow a negative up too much, the film grain can become apparent. However, because film has a randomly distributed grain structure and not a Cartesian pixel structure, when you blow a film image up to the point where grain becomes visible it is often not nearly as objectionable as an over enlarged digital image.
Some photographers expose, process and print to highlight grain. Done properly and judiciously used, accentuated grain can be quite pleasing to look at. In fact, many digital photographers will slave over their computers to simulate film grain in their images.
In the end, it's all about the photographer's artistic vision. Some like to have "razor sharp" images. Some like grainy images. Many people do a little of each, depending on their mood.
For a hobbyist who is just starting out, 35mm. film should be able to produce nice, sharp prints for 90% of anything you want to do. If you want extra-sharp images, consider moving up to a medium format film (e.g. 120 film which usually produces frames 6 cm. square on the negative.) If you want images so sharp you could shave with them, larger format is probably in your future. (4x5 in. or even larger.)
For now, stick with your 35mm. Learn it and understand how it behaves. When you get more experience you can decide whether you want to move up but, for now, your equipment will probably serve you well.