Hi, my DC system started out with what you're contemplating and it was completely inadequate. I have the 2hp Harbor Freight DC unit, with the Wynn 1micron filter and a separator barrel, all hooked up with 4 inch Rockler expandable hose. Very similar to what Mike has. The DC unit, on sale, cost $183 with the 20% coupon. The Wynn 1micron canister filter for it was around $140 as I recall. The HF collector has a 5 micron bag that comes with it, which is OK if you roll it outside and wear a dust mask at all times. A bag system can only go down to 5 microns (never seen one finer), so in the end you should get the canister filter, which also has much higher air flow.
Some folks have blocked the filter bag side of the Harbor Freight unit with a shop made lid and redirected the outflow outside, which may be OK if you live in the boonies, but unacceptable in more crowded areas. The canister filter greatly increases air flow through the system. Cleaning it out is a matter of blowing compressed air back through the outside of the canister to loosen the dust, causing it to fall down into the bag.
The chip separator (the extra barrel in Mike's pictures) will take out the vast majority of the larger dust particles, but the fines stuff is what does all the damage to your lungs. That's why it's so important to filter down to 1 micron if the air is going to outflow back into your shop. The chip separator also catches screws, nails, small chunks of scrap, and other items that can damage the impeller on the DC unit. These also make an un-godly noise when they hit. Lots of YouTube suggestions for making one of these.
Later, you might also get a passive air filter that hangs near a wall and which you run for about 2 hours after you close up shop. This circulates all shop air and removes the fines. It is in addition to a DC unit, not instead of one. WEN makes a nice one that is going for about $120 that has the same specs as most of the ones 3 times its price. Has a remote timer and 3 speed settings. Filters are cheap too, but can also be blown clean. Amazon has these.
I found a battery operated respirator mask at Rockler that I like very much. It uses 4 AA cells to drive a fan that sucks air in through a filter. The poslitive pressure on mine also blows a little air across my glasses so they never fog. I use it much of the time, but at least get some of those disposable masks that have elastic behind your ear to hold them in place. No cutting in my shop without a mask.
As you can see, you are going to eventually need about $500 of basic gear, and the HF 2hp unit (on sale) is the place to start. My shop is divided between a shed and my garage, and each has an HF unit, got two on sale. I'm still trying to unload my former system, which was barely passable compared to the new one.
I am a throat cancer survivor, and some wood is carcinogenic in the throat and lungs, that's why I take dust collection so seriously. The EPA did some studies and found that the worst wood dust conditions are in home workshops, and that these rarely meet basic clean air standards.