15 year old unit is about average for lifespan, so it's understandable they suggested to replace. (Source: ASHRAE Equipment life expectancy chart; google)
From my experience, with that low of electric bills, even if we selected a less efficient option, it would be worthwhile from a life cycle cost effectiveness standpoint. (Payback from low electric will not pay for the premium in cost) SEER/HSPF is how the units are measured, which is flawed but at least puts things on the table as similar. higher number is better. If you get the performance in EER or COP it is much better as it follows direct conversion rates.
In my opinion, get prices for one step up, etc. and see difference of SEER and HSPF compared to the price. General rule of thumb, (which depends on environment and usage) is that 1 SEER point is around 50 dollars a year of savings. more savings where it runs more often, less savings where it runs less often; thus likely you're looking at if it costs more than 750 for 1 step up in efficiency, it's not worth it with a simple payback, and if you are investing the difference in cost, it never really pays back unless it's very low cost (somewhere in the sub 400 dollar range for an increase in 1 step). (not related to electric strip resistance heating, which is what you want to avoid if at all possible, but you still want to have just in case-This is Emergency heating; this is what the poster previously was mentioning with the NEST thermostat)
Final question about looking into anything else: Not really, any other options are more sophisticated and cost more. a simple heat pump system is the way to go for cost, and ease. with only 120 in electric cost in the winter I'd say you're likely doing just fine with what you have and don't need to look into insulation or windows, or even leakage. Your current thermostat probably works just fine as well, but always good to confirm how it operates.
TLDR; Likely grab the cheapest heat pump system, which may still be better than what you have due to increases in efficency, and a programmable thermostat for it (like NEST; but it may come with this option!) to confirm it uses heat pump as much as possible before it ever thinks about turning on the strip heat.