Website hosting
own server, but it will be more profitable to host the site on a VPS or VDS. What exactly to place depends on how large an influx of clients you have and how long you want to use this server.
If you are going to use the server on a permanent basis, take VDS. It has better characteristics than VPS and will not break under a large influx of customers, it also has protection against DDoS attacks.
If the site is created by an ordinary user country email list or a novice programmer, or if you need to show how the site that you created to order will work, then feel free to rent a VPS. VPS is great for hosting a website for a short period of time because the payment is hourly and it can also be quickly configured.
Mail server
Every company has a need to send letters to its customers. This is necessary for the purposes of advertising, notification of changes, and so on. It would seem that you can freely use the same Google or another mail service, but the best solution would be your own separate server.
Thanks to your mail server, you will be able to send out mailings and control all the letters that you receive. For example, a partner can write to you by mail and if his letter can get into spam when using the mail service, then you will not allow this on your mail server. This is due to the fact that some IP addresses get into spam due to constant mailing, which is carried out from one server.