Cheap Web Space, Domain Name:
Web Space With E-Mail, PHP/MySQL.

Solution

Forwarding e-mails includes forwarding spam. That spam is recognized by recipient servers, so that your domain will be blacklisted by them, because it has sent the spam. The recipient does not care whether the spam source is not your server. After all, your server did send the spam mail to the recipient by forwarding it.

Instead of forwarding mails including all spam, you should create your own mailbox on the server and collect mails in that mailbox. There you can add spam filters to remove or mark spam. If you insist on forwarding mails to another provider, we recommend to use their POP3 collector for e-mails. It will collect all mails from your local server mailbox on your domain. The advantage of that configuration is, that spam won’t be forwarded and your domain won’t be blocked for forwarding spam.

Here you find instructions on how to use e-mail collectors of widely used e-mail providers:

T-ONLINE
T-Online only offers its collective service for a select few providers and prevents you from making your own settings. We therefore recommend collecting your e-mails here in your own domain in the mailbox and managing them there with webmail or an e-mail program such as Outlook, Thunderbird or Apple Mail.

GMAIL
https://support.google.com/mail/answer/21289?hl=en

GMX
https://hilfe.gmx.net/email/einstellungen/sammeldienst-einstellen.html

WEB.DE
https://hilfe.web.de/email/einstellungen/sammeldienst.html

OUTLOOK.COM (hotmail.com etc.)
https://support.office.com/en-us/article/Add-your-other-email-accounts-to-Outlook-com-c5224df4-5885-4e79-91ba-523aa743f0ba

It is even better to avoid forwarding altogether. There is not legitimate reason to forward mails, because all mail functions you need are provided by your web space here, including webmail.

Overview of frequently asked questions