You can generally push negative films one stop and still get very good results, although you will probably add a tiny bit of contrast. Beyond one stop, you're going to get degraded images in some way. But some films will push better than others. Check with the pro lab you plan to use and ask them which "pro films" they recommend for pushing. They may tell you a specific 160 film pushes fine to 640, while another one doesn't.
I have pushed 100 speed Ilford Delta Pro (B&W film) to 400 (2 stops), for a very slightly finer grain look than the Ilford 400 Delta Pro film at normal speed. But I did add contrast, which made the negatives harder to use. Today, I often shoot the Ilford 400 at 800 (1 stop push) with no problems. The thing to do is to test different films at different speeds. Determine what kind of look you want, then use that film and speed.
The high speed films will give you large grain, but that's a look in itself that can be used to your advantage. Although, if you're shooting with 35mm, big grain can be a problem. Consider getting a used medium format camera. Big grain on medium format can be very attractive. Also keep in mind that manufacturers often exaggerate film speed. The 3200 speed films are really 1,000 or 1200 (but are capable of being pushed to 3200). In your case, with the Fuji 800 speed film, you might have gotten better results with a 640 setting. Finally, keep in mind that digital shooters don't get grain -- they get noise. They have to buy PhotoShop plug-ins to add film grain. Why? Because having the texture of grain just looks better.