I presume that you want each apartment to have its own “self-contained” and “independent” heating unit. This pretty much excludes a central boiler in the basement to provide steam heat or a central multi-zoned oil, gas, or electric hot water “burner.” You COULD, of course, use such a system if you have an ample basement and you and your tenants can come to some sort of agreement about how to fairly split the costs of running the central system. In the long run, such a central system would be the most economical to install and run. But there is really no easy way to determine how much energy each apartment is using.
The EASIEST to install would be electrical baseboard convective heaters. Each apartment would be responsible for its own energy use. The cost of electrical heating, however, is in most areas higher than gas or oil systems. As the landlord, however, that would be your tenant’s problem…
You could also choose gas hot air furnaces in each apartment. The main problems are proper venting and following the codes regarding keeping heat from combustible building materials.
Gas burners for hot water heat are now compact enought to be installed in separtate units of multi-unit dwellings. Oil burners are also fairly compact, but the problem is getting the oil up to the higher apartments…so you might as well forget about that option. Hot water burners, gas or oil, require a lot of plumbing and, even with the modern compact burners, a lot of space to install the furnace.
Thus, if your main concern is that each unit be self contained, I’d recommend either electric baseboard or gas hot air wall furnaces. If you and your tenants can agree upon a “communal” heating system, I’d go with a central steam or hot water burner in the basement. This communal heating system is what is used in many large apartment buildings (such as the “projects”) in New York City and other Eastern Seaboard urban areas.