Let me try to explain it as briefly as possible.
All electric heaters have the same efficiency (100 percent) because they just change electric energy to heat energy and send it out to the room.
We can classify all space heaters into two: Convection heaters and radiant heaters.
Convection heaters heat the air in the room and the air heats you so all the room has to be heated and kept warm. Example: Baseboard heaters, heater fans.
Radiant heaters heat objects by radiating light rays. They are more efficient for heating specific objects (like a person) because they don't need to heat the whole room to do that. Examples are quartz and ceramic heaters and all other space heaters with the red-hot radiating screen.
Radiant heaters will work great if you are not going to move around a lot. For instance, you sit in the couch and set the radian heater across facing yourself. You will feel warm even if the rest of the room is freezing. They are not that good if people will be moving in the room a lot. That's when you need a space heater that makes every corner of the room warm.
Another thing you need to keep in mind in radiant heaters can sometimes be risky because they have that radiating screen that gets too hot.

Thanks, tedred.

It seems that a radiant heater of some kind would be what I want, for this office area. I wasn't sure whether ceramic and quartz fell into that category. All I knew was that long ago I had a 1929 house that had a gas fireplace with a ceramic insert, which would heat up and glow and did help to heat the room nicely. So I didn't understand if that was how a portable ceramic heater worked or if there was another property to it.

We have two oil filled radiator heaters. They make no noise. One of our electric heaters makes a loud pitched sound. They work well in a small room. I have a large flat heater in my room. It kinda looks like a TV. That's my favorite one, it works well on low and is silent.

As tendred says, all electric resistance heaters are 100% efficient. In the US, a 15 amp domestic electrical circuit can deliver a maximum of 1500watts. You will see that nearly all heaters will deliver a maximum 1500watts of heat, regardless of cost. So if you're paying more than 10 bucks for a heater, be sure you're getting something for that extra money.

I would avoid the gas furnace if you can. We only use space heaters and electric blankets. We had a way above average electric bill a few years ago when we heated with the heat pump. Luckily the electric company let us make payments over 2 months to pay for one month. We only use window a/c units in 3 windows of the house. It takes some getting used to. Either the house is kinda hot or kinda cold when we get home, but it only takes 15-30 minutes to get comfortable. We save hundreds of dollars a year or maybe a thousand doing it this way.

I suppose that since all electric heaters are equally efficient, the question is really whether one type or another is better at dispersing the energy as desired. So it seems that the radiant heater will do what I want -- make me warm without having to heat the whole room.

My electric bill runs high anyway due to heavy computer use in the home; I am not sure that using a space heater will save all that much if any money vs gas.

Zachey, I am confused by your comment . Why avoid use of gas to heat? It is inexpensive right now. Then you say that you have a heat pump. You have duel fuel central heat?

I used two lasko infrared heaters the last couple years along with a green heat one. The combination if two of them did good till it hit in the 20s. I tried tell of the lasko ceramic heaters already and they had no effect . I don't trust many of the heaters but those ones looked the safest and built well. I was really badly with them since the air circulation was good with two of them on.

"We had a way above average electric bill a few years ago when we heated with the heat pump."

It sounds like the heat pump was not working correctly and you were heating the house with the auxiliary heat strips.

It is usually cheaper to just heat and cool the one or two rooms in which you spend most of the time. But I question how much cheaper if your heat pump was operating at peak efficiency.