Would like to replace existing non-programmable one.

Hi, Not an expert, just a programmable-thermostat user. My landlord
recently bought and installed a "Lux" brand programmable, and it has
worked about 99% of the time. It's the 1% that'll get you - a few
times now it's "forgotten" to heat - the inside temp has gotten down to
55 or so. Once you manually bump the temp up a degree, it "remembers"
and kicks on and then it's fine. This has only happened 2-3 times in
the 6 months we've had it, but if I were buying one, I'd definitely
look for a nicer one. I've heard Honeywell is a good brand, but you
should wait for more opinions on that, or maybe look at Consumers
Reports.
Good luck (but no Lux),
Andy