You need a single stage press. The press clearance should be sufficient that there is enough space to seat a bullet in the case mouth without having to do gymnastics.

Most single stage presses can reload up to 375 H&H length, if yours is longer, you need a 50 BMG style press, like this Hornady. This is great for cartridges with an AOL over 4 inches.

The press should facilitate primer disposal. A press from which primers just fall to the floor is a pain where you don't need a pain. The primers from decapping must either drop into a tube, or fall into a primer catching tray on the press. There are many makes of press out there, each does it's thing a little differently, just choose one that can catch the used primer for you. All the presses pictured here have acceptable primer disposal.

Note that the old Lee O-frame and C-frame presses do not have any type of used primer collection. Avoid those, unless you want to use one for a dedicated station that does other than de-prime.

The reason I say you should have proper primer disposal on the press, is that if there is not, the residue from the spent primer falls down the sides of the ram, and sticks to it. It is highly abrasive, and over the course of time, will cause excessive wear between the ram and the frame. Aluminium frame presses are more susceptible to this type of wear, ie : they will wear out much faster than a cast iron frame.

If all you can get is an aluminium Lee O-frame press, don't worry, just use it to get started.

Make sure you have the right shellholder for the caliber you want to reload, for your press.