Broaching effort is proportional, especially manual. Presses aren't sized by throat depth alone, tonnage is a factor, you can expect enough power in a press tall enough for your workpiece and size of broach.
Be aware, the broach length is added to part height. The un-toothed starting guide enters minimally.
Most important factor is to not expect pushing through in one shot. I'd avoid purchase of a small arbor press, I have 4, all manual and 1 pneumatic-hydraulic 60 ton. They are chosen by which is smallest to do job in question; but larger is better than too small.
Adjust the ram clearance to a minimum over entire stroke, and lubricate with decent bearing grease, gear lube, or way oil. All have good film properties.
If you make a bushing, ensure width has least sliding clearance possible, depth must accommodate shims associated with using that broach. They are designated by letters, increasing with thickness to achieve depth. Only the smallest broaches generate full depth in a single pass.
Ram must be retracted every 2-3 maybe 5 teeth, allowing it to right itself - eliminate binding and breakage.
There is more than just cutting going on; apply plenty of cutting oil to teeth, spine AND and bushing. Moly-disulfide compounds work best, to combine cutting action and this lubrication.
Brush chips from spine and the teeth before re-inserting.
A box or bucket below is needed and will catch chips and the broach.
Used arbor presses aren't rare. I expect half available were found too small...the littlest are assembly tools of light interference fits, not what I'd call 'press work'. A clear sign is ram has a mushroomed head, trying to eek a bit more power. (Probably not same guy who paid for it!)
If bought used, ensure end is square. It's useful; face it off, bore a hole and a setscrew across to hold "tooling". 1/2" and 10-32 is OK. You'll thank me repeatedly for that tidbit. Should be, yet don't think that is ever a feature in a commercially made arbor press.
I like tapping 2 holes of opposed corners the bed plate as well.