I waited far too long to get any dust collection, in part because it seemed like to do it right required a lot of money and space. I've since come to the conclusion that a small cheap dust collector is way better than nothing at all. I've just got a small 1 HP dust collector, although I've added a canister filter and super dust deputy cyclone to it. It's made my shop time more enjoyable, especially with using the planer. I only use it with the table saw and planer, since I don't have a lot of other large tools.
Do yourself a favor and put it high on the list. Personally, I think it's a requirement once you have a jointer or planer. Even if it's just the harbor freight one to start, although I'd try to find something with at least a 1 micron bag.
I felt like I "needed it" as soon as I was able to work inside my garage, rather than dragging my tools out to the driveway. To be honest, I still only have a DC connected to my table saw, and generally use a shop vac with my orbital sander. I still move my jointer & planer outside, just because they create huge volumes of shavings. A respirator is good to have, if fine dust collection is a problem. But catching at the source is much better.
Sorry to sound like a broken record. I do not have wood allergies. I’m just a regular person. I was not diligent enough on dust control early on. I now take medication every day and will for the rest of my life.
We can’t all do a perfect job of collecting spoil. I do always recommend that you do the best that you can in the room you have and with the budget you have. I also start all responses to the question of “what tools should I get first?” with number one being dust collection.
I am not some kind of dust collection wacko that thinks anybody who doesn’t do perfectly with their dust collection system is doomed to a horrible death. Let’s just use common sense and do the best we can :-)
IMO, DC is very important! Obviously, the crap you breathe in isn't good for you but, how about the time you spend cleaning up all the dust you're making instead of continuing to work on projects? And, to boot, There's some pretty inexpensive options out there!
Again, just my opinion but, you need the big 3 first. Table saw, jointer, and planer. Coming in at 3.5 would be the dust collection. I'd rather work on projects that clean the shop.
As an additional note, the more energy you invest in good dust collection the more enjoyable spending time in your shop is. You'll note I said energy, not money. As I said before, there's lots of inexpensive options out there.