Forum & Donation Badge Integration

I run www.derechtsepen.org and would like to turn our occasional donors into an engaged community. The plan is to launch a fully-featured forum under the same domain (e.g. /forums or a sub-domain) where visitors can register, talk and, importantly, donate right from their profile.

Here is what I need:

• Forum platform – I’m open to phpBB, vBulletin, Discourse or any other solution you feel is best. Speed, stability and ease of moderation are my only must-haves.
• Visual match – the forum has to inherit the current look and feel of derechtsepen.org so the transition feels seamless.
• Donation flow – integrate PayPal and Bank Transfer options. After a successful payment the member should instantly receive a visible badge: €10 badge for €10 donations, €100 badge for €100 donations, and the logic should be easy for me to extend with more tiers later.
• Badge display – badges must appear next to the username in posts, in the user profile and on a public supporter page.
• Admin tools – a simple backend panel (or plugin) where I can adjust badge tiers, review payments and manually award or revoke badges if needed.
• Clean hand-off – once everything is tested, please document the key settings so I can keep things running.

If you’ve done similar community + donation setups, let me know what stack you prefer and how long you’ll need—I’m keen to get the discussion board live as soon as possible.