There are many ways to hang a filter. This is mine.
First, I lay my filter, fan and any acoustic dampeners on the floor. I use anything available to sit them upon, in order to line up the connections. Gaffer tape them, then fast-clamp. This gets my entire assembly together on the floor.
I then lay a beam of wood along the top of all my stuff, and tie everything to it. Rope for the filter, and string for the bits that don't weigh a lot. Now I have everything tied to my beam (often a 2x2) that can be lifted and suspended as one unit.
What you are going to tie it too depends on the building structure. In the pic, I have used some strong wall brackets. You may wish to drill the roof beams from above to use long eye bolts. Me, I like to make a strong net frame for the plants, that reaches the roof. So it's all free standing, with no fixtures to the building at all.
So, you have your fixing points at high level, and all your stuff on a beam. Time for the rope ratchets. Just like you may hang lights with, these come in a few sizes, right up to Articulated vehicle straps. The filter sized ones should do. Using one each end, you can slowly raise the assembly, one end at a time, all on your own. Presuming you can take the filters weight while you pull up a few clicks on the ratchet.
Take it up to just a couple of inches lower than you want it, and use some proper rope to secure it. Now it's time to stop it shaking the building. In the pic, you can see some blue lines. It's elastic. You want some elastic that's too thin to work with one loop. 5mm bungie cord perhaps. You put a turn around your beam, and high level fixing point, pulling the cord as you do, so it's at maybe 30% of it's possible extension. If the cord was thin enough, it won't do anything. It should take a few turns before the beam starts to be lifted by the elastic cord. You can pull a bit of slack between the turns as fine tuning, which is why you want a few turns.
When the elastic is right, the whole thing can bounce. You can both push it up with a finger, or pull it down with a finger. Because there is no solid connection to the building structure.
Acoustic dampeners/mufflers/silencers, whatever, are good. Most of their work is done within the first 40cm. Equally, hard pipe is good. A short length of solid ducting can reduce the noise a lot. Just 40cm between fan and filter can make a big difference to the noise coming out the filter. On the exhaust side of the fan, you could line a tube with camping mat to further reduce noise reflections. But just pipe is surprisingly good. While a full on 600mm 'real deal' is really quite good.
As a closing note, fixing to the roof may use it as a sound board, amplifying noise. If the walls are brick/block construction they are much harder to shake(impossible though a bit of elastic). However, if using the wall bracket approach, don't fix to the top block of a wall that goes no higher, and then put the weight at the very end of the bracket(as in the pic). You could lever the block out. Just keep your weight near the wall, pulling the block down in place.
