Palm Beach’s reply is essentially correct if a little cryptic.
The main thing an owner needs to consider when dropping a claim is “Why do I need to own this horse?” which may be an entirely different thing than why a trainer wants to claim a horse for you.
Considerations:
Conditions – are there races where this horse can compete successfully? If he wins today, does he burn through his conditions? Is he a turf horse at the end of the season and the tracks are switching to dirt? has he been running against age restricted horses and has to run against older? Is he a maiden claimer and therefore the tag is probably inflated? Is he state bred? Does his best distance and surface come around every three weeks or do those races just not fill so you might even be waiting months to run him back? That just really scratches the surface. The really important question when you drop is do you have a plan if the horse is what he appears to be and not some big homerun that comes up once in a blue moon
Physical-- is the horse basically in one piece? Are the physical issues manageable? (This is why claiming trainers are down at paddocks when they aren’t running them–they are marking legs on the ones they are interested in. Some trade information with others who have had the horse in the past.)
Sex and age–really part of conditions. Fillies may also have some (but usually not alot) of residual value as broodmares
Personalities–some trainers will not claim from other trainers so you are SOL if you want a horse from that barn. Some trainers are leery of others because they have been burned before. Then there are trainers so good that few can move a horse up on them and trainers so bad that the horse may be an impending trainwreck and the guy doesn’t realize it but you will when you take possession.Some trainers are good caretakers but mismanage the horse so there may be an opportunity. If you watch the claiming game at your local track, there will be patterns as to who claims from who.
And these are just some things to consider…