What to look for when choosing a new bathtub?
The most common discrepancies in price between tubs, not counting accessories like heaters and jets, are due to four factors: style, depth, build quality and brand. A garden tub will generally cost you more than a simple rectangular built in, and a clawfoot is more expensive still, followed by "custom" installations like non-overflow tubs.

In the same style, the depth of the tub determines the volume and weight of water the tub must hold and therefore the dimensions and thickness of the material. More material == higher cost.

Even in the same style and depth, one maker may build their tub out of cast iron while another uses plastic, or even in the same material, one maker may double the thickness of the tub walls to increase durability and thus longevity (removing a damaged built-in bathtub is no small job; it can even require a full remodel because it requires re-tiling the backsplash).

Lastly, major name brands will command a higher price even if their product is inferior. Jacuzzi, for one, is a trademarked brand name that has apparently rested on its laurels; I was warned away from even their thousand-dollar tubs for quality reasons, but the tubs still cost a grand, cause they're branded with a universally-known name (so much so that people use the brand without knowing it's a brand, similar to "Band-Aid")

As far as actually what to look for, it depends on what you want. For an upstairs bathroom normally used by kids and guests, a standard Kohler, Moen or American Standard acrylic or cast built-in is fine. Cast iron is more durable, and holds the heat of the water well, but it'll be a beast and a half to put in place. For your own master bathroom, you can be pickier. The three brands I mentioned are names I trust, and they make tubs in all shapes, sizes, styles and pricepoints.