Should I add air ducts when finishing my basement or rely on space heaters?
Summary...  100% add the duct work.   It will be cheaper in long run, look better, and will increase resale value of the home.
Few things here:

Once you add those walls/ceilings (given it is not a drop ceiling) adding duct work will be very costly and messy.   This is sort of like running ethernet cable throughout the house, but air ducts probably have little chance of being under spec in your lifetime.   Adding a damper with access to manually turn it off and on is common.   (forgive the price here... usually about $15, just an example)

Most inspectors will not allow a place to be label &quot;finished&quot; without it being conditioned in all rooms.   This depends on where you live.   So what I am saying is... before you ask this question on here and research options - Have you asked your inspector?   I can't think of one place that would allow me to &quot;finish&quot; a basement (that's something I have done more than any project) and not require each room to be conditioned.   I have had some inspectors require that I condition (add ducts) to the unfinished areas if any of the basement is considered finished.    Yes I said that right - I have had to put ducts in unfinished storage or laundry room because I was getting the rest of basement signed off on.

It makes no sense to have 1000 sq feet done by space heaters.    That's just too big.   To do it right you would need a few faux fireplaces with their own safety and shutoff devices.   These would probably require special electrical.   Running ducts in an unfinished space is cheap.   Doing &quot;nothing&quot; sounds cheaper until it isn't.

Even if you ignore all of the above just do it for the resale value of the home.   If I were scoping out a home to buy I would notice the lack of duct work in a basement that size, would assume I would rip apart a lot to fix it and would adjust the price in my head.   Worse though is that I would assume other things weren't done right.   And even worse to the non-handyman is that the &quot;fireplaces&quot; or &quot;heaters&quot; probably make the finished area look a bit tacky.


Note: If someone were only finishing a small part of their basement - two small rooms (workout room + whatever) I could see the justification of not adding ducts as the bleeding of the heat would be costly and not efficient.   This probably gets into what % of the basement is being finished.   I think once you get over 60% or 500 sq ft the answer is probably yes you should.
Note to the note:  In the case above if you don't condition those two rooms, likely the city will not consider that finished space when you are selling the home, no matter how nice it looks.  (this also could be actual home square footage in a walk out basement)