The standard, and who follows it
Nearly every card you have ever held is 2.5 x 3.5 inches: Topps and Panini sports cards, Pokemon, and Magic: The Gathering all print at 63 x 88 mm. Yu-Gi-Oh runs slightly smaller at 59 x 86 mm - which is why it uses its own sleeve size - and vintage tobacco-era cards were smaller still.
The standard survives because the ecosystem is built on it: penny sleeves, top loaders, nine-pocket binder pages, deck boxes, and grading slabs all assume 2.5 x 3.5. Print a custom card at standard size and it drops into any of them.
Thickness: the spec people forget
Card thickness is measured in points - thousandths of an inch. A 1950s Topps card is around 12pt; modern base cards run 14-16pt; premium and slabbed-style cards go thicker. Thickness is most of what separates a card that feels real from a home-printed one: printer paper is roughly 4pt, a third of a real card.
Snapshot prints on premium 16pt coated stock - the weight of a modern retail card - which is why custom cards sleeve and shuffle like the ones from a pack.
Bigger formats for display
Beyond the standard, collectors know 5x7 box toppers and jumbo promo cards. For wall display, Snapshot prints the MEGA card at 11 x 15.4 inches - the same card design at poster scale, popular for senior nights and bedroom walls. For everything meant to be held, sleeved, or traded, stay standard.