You may look into installing a vent in the furnace room if you have one next to that area. This may allow you to draw heat from the furnace room, into your finished basement area, up the stairs to the first floor and back down again. Depends on where the return is and how things are "zoned".
If you do install on the drywall get as low as possible so the heat sweeps across your comfort area to the nearest return. Heat rises... Install dampers so you can tweak the amount cool feeding into the basement during the summer. Follow the path of airflow and calculate as much as you can. In tools such as Revit (warning: steep learning curve) it is called a load analysis; though, it can be done back of the hand.
If you already have a ducted system, I wouldn't install an electric heater. Nice for a small area such as a desk/bathroom, but do keep in mind how they affect humidity.
This is going to be sort of a comment, or at least not a complete answer.
When designing the system, the goal is not to create a breeze through the space. The goal is to control pressure equalization in such a way that the air is mixed and dehumidified (conditioned).
Having one large return at one end of the space, and a large return at the other may work. But it's not going to be as efficient, and will require maintaining an open area for which the air to flow (no closed doors).
Let's back up a bit, and think about how the system works...
The fan (or blower) is going to create a high pressure area "in front" of it, which causes the pressure in the supply ducts to increase. The higher pressure air flows from the supply ducts, in an attempt to equalize the pressure between the supply ducts and the rooms. At the same time, the fan (blower) has also created a low pressure zone "behind" it. The higher pressure air in the rooms is forced into the return ducts, in an effort to equalize the pressure between the rooms and the return ducts.
So the system works by forcing conditioned air into the rooms, and having unconditioned air pushed into the system.
Wherever you have a supply duct, you want to have and unobstructed return duct. Otherwise you'll end up with a high pressure area in one place, and a low pressure area in another.
In your example, if you have a single supply duct feeding the kitchen, and a single return in the bedroom. What happens if the bedroom door is closed? In fact, the bedroom door in your drawing would have a tendency to be pushed closed, if you installed the system the way you've described. You'll be creating a high pressure zone in the kitchen and living room, and a low pressure area in the bedroom. Which means the door could be closed by the pressure differences.
You'll want to install a supply and return in each separate area. In your case that would mean installing a supply and return in the living room/kitchen, bedroom, and storage area.
Unfortunately, duct design is a bit of science, and a bit of art. Covering all the information you'd need to know, would be nearly impossible in this short answer format. In my opinion, duct design is not a job for an amateur. At the very least, you'll want a pro to assist in that aspect of the job.
I know I've rambled a bit, and I'm sure you don't want somebody to tell you not to do it yourself. But in my opinion, it's better to have it done right, then to have it done cheap. Aside from all that I've mentioned. It's impossible for somebody to design a duct system without knowing the equipment you're going to use, or the actual dimensions of the space. So there's no way anybody on this site could provide a duct design for you, with the information you've provided.
My advice... Get an HVAC contractor to design the system for you, then you can do the work of installing it yourself.
Best Answer
I think you have a good handle on it.
"If correct, is it a big issue if it is blocked/clogged?"
Yes and no. If blocked, air will be drawn into the house through chimneys, bathroom/kitchen/dryer vents, leaky windows, etc. That air would be cold and uncomfortable. But not dangerous. It will eventually move to the furnace room.
Clean that screen and the air drawn in will be used by the furnace and water heater and not cool down the house.