My suggestions:
1. Forget about spinets; strings too short; actions too small. Techs don't like 'em because they never sound very good; are hard to tune; are hard to work on (pulling the action out is an ordeal).
2. Look for a piano 45 inches or taller; this is a "studio" size (or larger). Longer strings; much better sound; much better action. Only a little taller than a spinet; really insignificantly "bigger."
3. Look for a used Yamaha or Kawai; there are lots of them around; they are well-made pianos, reliable and can sound great if well-tuned and voiced. Look for a piano that is 20 years old or younger; it will be much less than a new piano and will likely have many good years left. You can determine the age of a piano by its serial number, using the Pierce Piano atlas (someone contributing here will have one to look up the number for you) or a website with such information (do a Google).
If you cannot tell whether the piano you are thinking of buying is in tune, can hold a tune, or the action is excessively worn, have a technician inspect it (for a modest fee). Depending on where you live, you should be able to get a 20 year old studio piano for somewhere around $3000; possibly significantly less.
4. Piano tuning fees vary from perhaps $75 to $150 for a single tuning, not requiring any pitch-raising or action work. This depends on the market and the tuner's skill level. If your piano hasn't been tuned once or twice a year for some time, it will need pitch-raising and frequent tuning the first year to get it to proper pitch and stable in tuning.
5. Depending on your location (climate) you may have to buy a humidity control system for your piano in order to keep it in tune and playing well. So you need to allocate some resources each year for maintenance, or your piano won't sound good.
Topic: Buying First Acoustic Piano