Books are fine up to a big point. Better: ask around in the neighborhood the homes that use wood stoves for more than supplementing a furnace, or for entertainment fires. Look for woodburners with woodsheds and/or nicely stacked piles in their yards. Ask them how they do it.
$2000. is a high budget for a quality used wood stove. Leave room for your liner, wood, accessories (such as a hearth extension if you go with a free standing stove).
Spring and summer are fine times to find good used wood stoves. People are moving, getting a new stove, or just don't want thye effort of heating with wood. Look at the "Stove Rating" section of hearthnet.com for user's experience with brands and models. Most have had good luck with Woodstock (cat), Pacific Energy, Jotul, Morso, and others. Strong opinion: stay away from Vermont Castings' products.
Yes, a lining is mandatory for code, insurance, safety and efficiency. It will cost about the price of a stove IF you do it yourself. Go SS.
Decide with your family how they want the stove to look: cast, soapstone, steel. Non-cats are simpler to run, but catalytic stoves are more efficient with longer burn times ( we have one of each for 24/7, 100% wood heating), If you can find one, get porcelain.
Inserts are not efficient heaters compared with a free standing stove while the cost is the same. Visit dealers and fool with the stoves you like. Many dealers sell at discounts now their returns, trades, "scratch and dent" stoves.
Size: go slightly larger than the specs of the stoves for the space you need heated.
Finally as was said, NOW is the time to get your firewood: scrounge, harvest, or buy CSD (cut, split, delivered), or log length. Learn what species in your region burn best. Most firewood sellers are hard working and honest. Ask.
JMNSHO