Max (and most other modellers) also have rendering support, so they can render your scenes out to images -- you don't need to capture the screen to get your models into an image.
The process of creating sprites from a model is essentially invoking the modeller's renderer with the desired settings (for lighting, anti-aliasing, and what have you) repeatedly at every desired camera angle. The settings you have to select really will depend on the desired effect you want in your sprite images -- you'll have to experiment.
Most serious modelling tools have scripting support, so you can create scripts to automatically render the scene from all the desired camera angles and possibly even stitch the resulting images together in a sprite sheet. Here's one of many available scripts for Max, for example.
Since Max is quite expensive and you don't currently own it, you probably don't want to drop the cash on it. You can use Blender, which is free and has Python scripting support that should allow you to build an automated workflow for your sprite rendering. Just make sure the assets you purchase are loadable by Blender -- try to get a sample file from the author first and make sure everything works well (this is a good idea even if you don't use Blender, note).