I assume you have 12 or less customers.
You live at home so you expenses are low so you will be able to build up a suitable cash reserve rather fast.
So in your case you I would collect at time of service. Many types of large business' do this.
Most of your customers will be elderly and at home. They will know what time you mow and will be home when you get there. I have had customers miss a week and catch me the next week. You won't go under getting $35 one week late.
Also had customers approach me worried that they would not be able to pay because they were going away on vacation. I told them don't worry you get when you come back.
However I have seen many LCO's get hosed over when a customer goes one month late, and before you know it the LCO has been mowing for two months and stops service for non payment, after he's done 8 to 9 mows.
Best to always keep things simple. Now when you start to get commercial accounts and they pay you by check and want to pay monthly. On those I send out an invoice the next day after the last service for that month. So that means I invoice on the 25th instead of the 31st.