Can my customers pay a deposit now and the rest closer to travel, or do they have to pay the full amount when they book?

Yes, you can usually take a deposit now and collect the balance later, but whether it is safe to do so depends on what is being booked. Hotels with free cancellation are the easiest, because the supplier does not need the money until close to the stay date, so you can hold the room and collect the rest before that deadline. Flights are different. Once a ticket is issued the airline wants the whole fare, so offering a deposit on a flight usually means you are covering the difference yourself until your customer pays you.

On the website side this is a setting. You can set the deposit as a share of the booking, pick which products it applies to, and set when the balance falls due. The customer pays the first part by card at the time of booking, and their confirmation shows what is still owed and by when. The balance can be collected with a secure payment link, or by charging the same card again if your payment provider and your local rules allow a card to be stored.

The part to watch is the gap between your balance date and the supplier's own deadline. If the customer does not pay in time, someone has to cancel or pay, and that someone is you. Most agencies handle this with automatic reminders and by cancelling a few days before the supplier's free cancellation date. Whether you give the deposit back at that point is your own policy, so put it in your terms.

Check with your payment provider whether it supports payment links and repeat charges, then decide which products you are happy to sell on a deposit and set your balance date safely ahead of your supplier's.