Smaller enlargers that can accommodate 35mm and 120 negatives will get you started, and older models are relatively inexpensive if you buy them used on eBay. Models that used to cost hundreds or even thousands of dollars can now be had for under $100. Look for a relatively small and lightweight model such as the the Omega B22, B6, or B600, which were popular workhorses and are easy to move out of the way when not in used.
The Durst M600 and Beseler 23C (great for medium format) are also solid choices but they're bigger and heavier. Read the information carefully and make sure negative carriers for your size film are included. You may otherwise have a tough time finding them. Same thing with the lens. An enlarger lens is necessary but may be sold separately. If you're using 35mm film, get a 50mm lens. If you're using 120, get a 75mm lens. Beseler, Nikon, Rodenstock, Olympus and Schneider are all reliable brands.
Warning! Stay away from any Vintage Federal enlarger, even though they are plentiful on eBay. They are infamous for overheating and burning negatives (taken from personal experience and online discussions).
Easel does it
You will also need an easel, which holds your printing paper in place under the enlarger. Used easels are plentiful on eBay, but a two-sided 4-in-1 easel (which has places for pocket, 3x5, 5x7, and 8x10 prints) is a cost-effective, space-saving investment. You will also need a Focus Finder, which will help you make sure your prints are sharp.
You'll need at least 3 trays for print development. 11x14 is a good choice and will cover you for most prints. A larger tub such as the 12 Quart Sterlite Red Dishpan Basin, Multi-purpose, 15 3/4" x 12 1/2 " x 6", which can accomodate 11x14-inch prints, will be needed for washing. You will need to drill 2-3 holes on the side about 2 inches from the bottom so the water will drain. You'll also need tongs to move prints from one tray to the other. You'll need a graduate to measure out your liquids, a funnel, a stirrer, an accurate thermometer, and at least 3 brown jars to store the chemicals.
Timing is everything
Finally, you will need a timer, since printing and processing times need to be carefully set. Spurge on this and get a Gralab 300 60-minute Darkroom Timer. It controls your enlarger or can work separately for timing processing at the flip of a switch.
Safelight at first
While you could buy an amber darkroom light new or used on eBay, a plain 7-watt red bulb in an an existing light fixture will do the job just as well and save you some money. You can find one at your local home renovation supplier, or you can order a lifetime supply of this Novelty Light, 7.5-S11 Commerical Grade S11 Ceramic Replacement Bulbs, E26 Medium Base, 7 Watt, 25 Pack (Red). I used that as my only darkroom light for many, many years. Want to step up? The Premier 10x12 Safelight is the industry standard.
Other miscellaneous gadgets you may or may not need:
Paper trimmer : A great tool if you're making odd-sized prints, and worth getting for cutting and matting prints for framing. If you only need a strip of paper for a test strip, use scissors. You already have them.
Dodging kit: These are essentially cut out shapes at the end of a thin stick that you move around as you're printing to selectively lighten areas of the print. You can make 'em yourself with a scissor, tape, cardboard, and an straightened wire hanger. They're almost impossible to find new.
Chemicals? Paper? Yeah, you'll need 'em! More about that in upcoming guides.