If I paid and moved in on the 18th of the month is that when my rent period begins when there is no written rental agreement?

When a "rent period" begins is governed by the agreement of the parties (landlord and tenant), whether expressed orally, in writing, or by behavior/action.

When there is no explicit agreement, oral or written, to the contrary, look to what was evidenced by behavior. If you paid you full rent on the 18th, then the rental period would run by 18th of month 1 to 17th of month 2. If you paid a pro rata share of the rent, it may be the rental period commences on the 1st of the next month. For example: the 18th is 60% of the average month, which means that the remaining 12 days are 40%.

Say your rent is $1,000/month. If you paid $1,000 when moving in--so a whole month's rent--then the period would run 18th to 17th. If you paid only $400, though, that would be the payment for the 19th to 30th or 31st--i.e. your rental month begins on the 1st, and when you moved in 60% of the way through the month, you only paid for the remaining 40% of the month.