Typically, if you can prevent drafts with an enclosure, and your heated bed gives off some heat, that will be plenty to get the insides up to a decent temp. Yes professional 3D printers do have extra heaters, but I don't recommend that, you will cause a fire hazard, and you will cut the life of components that need to be inside. 3D printers that use the bed as a heat source usually have fans that turn on when temps get too hot.

For filters, I use a laser particle counter, and have no problem with a hepa filter removing particles. Some use a carbon filter to remove the smell as well. The problem with a hepa filter is they take a pretty strong fan to move air through them. But enclosure, fan and filters are pretty common with many printers today. I would use the same filters they do, since they have already been proven.