As you've already mentioned, there's a big difference (including price) between a shop vac and a dust collector. As your shop grows, you should budget for a DC in the future.
Meanwhile, as previously posted, any dust collection is usually better than none. A shop vac is relatively inexpensive, and you'll always have use for one in your shop, for general clean up, and for use with handheld tools, such as routers and sanders.
Make sure the shop vac has a good filter (preferably HEPA-type), or it will end up blowing a lot of small particle dust back out into your shop (and lungs). BTW, IMO the box fan/furnace filter setup is a mixed blessing. While it does indeed trap a lot of air borne dust, a furnace filter is not fine enough to filter the smallest (and most dangerous) particles, which the fan blows back into the shop air.
From what I can tell, the DW745 dust port is sized for a shop vac hose, so the simplest solution is to connect the shop vac hose directly to the saw. A better solution is to get a Dust Deputy, connected between the vac and the saw. You'd be amazed at how much dust it traps, which will make keeping your shop vac filter clean a lot easier. An alternative to buying a Dust Deputy would be making a Thien separator.
Finally- or first- get a good respirator mask. Wood Whisperer has some good recommendations. Good luck, and keep cutting!