Evaluate the heating system, and determine how much longer it will function adequately.
If it has less than 4 years left in it, go ahead and replace it now. Much less of a headache to deal with it while it is empty than while it is occupied.
Replacing the windows yourself is a fairly straightforward task. Pop the trim off with a prybar or 5-in1 tool and carefully work your way around till window itself is exposed. Remove the glass and screens from the old window, or take it out as a unit. Vinyl double pane replacement windows drop back in with a minimum of fuss and effort. Place them in, shim to level, screw them to the jamb, and caulk to seal. Replace the trim...
Hardest part is measuring correctly on the existing openings. Drop by your window supplier with a picture of the window and ask how to properly measure it. They should be happy to help you out, and if not find someone else.
I'd look at replacing the windows that are in worst condition, and/or face the worst elements or street traffic. New windows will make the place more efficient, but also reduce the traffic sounds etc. which can be used to attract better tenants. You can always replace the windows one at a time, and after you figure out how to DIY them you'll have no problems tackling them.
Changing out a few windows every other month or so is a lot less disruptive for a tenant than a heating system upgrade. I'd lean towards doing them on the half you live in first, as it will lower your direct costs sooner.