I started T well after menopause (I'm 62, and started about a year ago), and it's going fine. You'll need to work closely with your doctor, and it would be best to find one with real experience with this stuff, if you can, because what's a low dose for one person may be a high dose for another. There's a lot of variation in how people react, and there's not much actual data on men who transition later in life. I see my doc about every three months, and she monitors my blood work very closely; more for things like liver function, cholesterol level, and such than for the actual T level. It's hard to predict how T will affect an individual, but even on a low dose you're likely to get some permanent changes fairly early, most notably your voice; but you can stop if you find you don't want to go past a certain point. If you do stop, though, any gains in strength and muscle mass will eventually be lost.
Anecdotally, and based on my own experience, it seems that changes from T happen more slowly for older guys than for young ones. And given that bio men tend to lose muscle mass as they age, that may be one of the harder things to change. I know I have to work out pretty hard, and very regularly, in order to see gains in that department.