Reddit mentions of American Thermal Aquarium Thermometer Horizontal

Your water heater should have a built-in thermostat. Set it to the temp you want and the heater will turn itself on and off to maintain that temp.

If you meant thermometer, I just use this style that sticks to the glass: https://www.amazon.com/Liquid-Crystal-Horizontal-Aquarium-Thermometer/dp/B000633PU8/ref=zg_bs_2975477011_13?_encoding=UTF8&psc=1&refRID=3VCAYQ0V3WFSMTZVBB7P

I've tested it with my thermocouple temp gauge and they're accurate enough.

That aquarium is a perfect size for a single betta and plants.

I nearly always recommend EHEIM Jager heaters. They have adjustable thermostats and an auto-shutoff if the water level gets too low. They're also super reliable. The 50 watt is nearly always cheaper than the 25 watt and it works just fine in my own 5 gallon.

I like live plants because they do help with water quality. Care really depends on what type of plants you go with. Anubias, Amazon Swords and Java Ferns are super easy to care for and don't need any special substrate. Some others like Ludwigia and some crypts are much harder and prefer dirted tanks. Certain species require CO2 supplements and fertilizers other than fish poop. All live plants will need trimmed occasionally. Silk just needs wiped down when it starts to look dirty.

Water changes are even more important in smaller tanks. Remember, the solution to pollution is dilution. 25% weekly is good so fish waste doesn't build up.

I've used a number of thermometers, but don't really have a preference. The only thing I'd suggest is that you avoid the stick on kind. They work fine at first, but accuracy won't last long.