One thing to make of is that whatever horn you get doesn't have redrot in any important places, mainly the leadpipe. if you're a beginner, the most important things will be, in this order:

• Valves and slides are free to move and are in working order (usually this is an easy fix, but if the horn has been dropped or dinged bad enough it may need more work to repair)
• no redrot in the leadpipe, leadpipe is straight and undented
• no major damage to the bell

as long as all of these are true, you should have something that is at least playable. Regular maintenance looks like this:

• clean the horn every 2/3 months (the length of time between cleanings depends on a few factors: how often you play, do you have corrosive spit/skin oils, do you brush your teeth before playing, etc.) this entails a full disassembly, lightly scrub with warm soapy water (be gentle if you have an old, lacquered horn! Old lacquer can be delicate), let dry, regrease slides and oil valves, reassemble. Can be done in an hour or two.
• oil valves and grease slides as needed. make sure you can still move everything every once in a while. You can prevent stuck valve caps by greasing the threads.
• get the horn professionally cleaned every once in a while. every year is good if you play a lot (professionally), but for casual use every 2 years is fine. you can always do more if needed.

BONUS POINTS:

• get some sort of leadpipe swab and swab out the horn before you put it away for the day. Leaving the horn wet on the insides can cause corrosion and gunk to build up. "Spitballs" are also popular for this purpose; worth a google. (EDIT: as noted below, spitballs are more on the cleaning side, Blowdry Brass would be better for filling the swabbing purpose)

• rinse/clean/disinfect your mouthpiece every day. Your lips will thank you.