I've been using Collective (formerly Hyke) [https://www.collective.com/] which not only provides you your own Quickbooks account (to handle all invoicing) but also helps you set up your own S-Corp for better tax savings (if you're US-based) and navigate all the accounting duties. It's a monthly subscription service, but the time saved from not having to deal with accounting plus the tax savings from be set up as an S-Corp pays for itself. Just speaking as a happy customer for the past 18 months. They are extremely supportive and responsive; it's like having your own accounting team. In terms of invoicing, like everyone and you have mentioned, it does depend on the client. I usually invoice at the end of the month.

Feel free to message me for more guidance on getting situated as a freelancer and if you want to learn more about my experience with Collective. I was in your position and someone had explained all this to me instead of learning about it the hard way!