The first thing I do is run a hand along the inside edge and check the slope of the base. Too flat and you're sliding around like you're in a canoe, too steep and the water pools weird at one end. I also knock on the side, a dull thud means it's solid, a hollow rattle means it's thin acrylic that's going to flex under you and maybe crack at the corner in five years. Weight matters more than people think, both the tub's and whether your floor can take it full of water and a grown adult.
If you've got nothing to go on, start with a straight sided alcove tub in a plain white or off white acrylic. I know, I know, I'm the color person, but a bathtub is not the place to get brave first. It fits into almost any bathroom layout, it's the easiest to reglaze or replace later without redoing tile, and it won't fight the rest of the room while you figure out what you actually want on the walls around it. Where it does go wrong is when people try to match it too closely to a trendy tile color, a pale blue tub with pale blue subway tile reads like a hospital room, and a stone colored tub against warm wood vanities can look muddy rather than cozy. Freestanding tubs in bold shapes, copper, matte black, that stuff is gorgeous but it wants a bathroom with enough floor space to breathe around it, not a cramped rental bathroom where it just becomes something you bang your shin on. My mother has a beige bathroom with a beige tub and she will tell you it's restful. I think it's just beige. But she's never once had to think about whether it clashes with anything, so there's an argument there too.
Cast iron with enamel ages beautifully and basically forever, acrylic scratches if you're rough with abrasive cleaners, and both yellow a little under hard water if you never seal or clean properly. Wipe it down after use so soap scum doesn't build into a permanent ring, use a nonabrasive cleaner, and refinish or reglaze every decade or so if it's starting to look tired rather than replacing the whole thing, which is expensive and disruptive for no reason. Check for hairline cracks around the drain every so often, that's where leaks start first. Before you buy anything, measure the rough opening width, length and depth, and measure your doorway and stairwell too, because a bathtub that won't fit through your hallway is a very expensive thing to find out about on delivery day.