We obviously all have our favourites. If you want a good cross section of independent forum owners to discuss or research some more, try the Admin Zone at The Admin Zone
I've personally used many forum solutions over the years, but now there is still really only one for me that I personally use and also recommend and provide to my clients, which is - Removed - (my referral link) | (non-referral
link if preferred). I've been using Invision and its predecessors since 2002. I honestly just think it is way ahead of the competition, in terms of design, features, functionality, expansion and also speed. A lot of vBulliten owners switched to Invision for various reasons and users often switch back from Xenforo after trying it or the free solutions.
I use the self hosted version for multiple websites, but they also have a cloud-hosted version which runs on AWS S3. They have a time limited demo option available if you want to give it a test.
The Invision forum software itself is IMHO very robust and solid, whilst easily customisable. Honestly, speaking from experience, avoid the free forum software like a plague, they obviously have a market but are best avoided if possible, in particular if you value your user's data and want less or no spam.
Invision has a responsive design as you'd expect supporting mobile devices, it has drag and drop widgets, optional sidebars, rich media embeds, a built-in optional multi-calendar app, easy integration with third party services such as Google APIs like address lookup, Google Maps, Map Box, Send Grid etc and a built in promotion manager for scheduling featured content to social media platforms etc.
Invision also has strong GDPR functionality, a built-in REST API, Wordpress integration/authentication should you need them. The user profiles are miles ahead in terms of appearance, flexibility and customisation, everything in the software is permissions based, and there are the usual email, browser and PM notification options.
Invision is also cheaper than some of the competition, especially the new Node based solutions the cost of which is very high. They provide optional official bolt-on/add-on apps such as Gallery, Commerce, Pages (a database manager and article/wiki CMS), community blogs, a downloads/file manager etc if you need to expand in the future. Invision also has a reputable Marketplace available for third party addons, plugins and themes, both free and paid solutions.
You mentioned forum layout is an important consideration. The Invision forums app now has 3 types of layout, the traditional forum style, a modern grid (card) style layout and a modern fluid view which is more suited for smaller amount of forum categories. You can lock a particular layout or a theme, or let your forum members choose their preference.
You can set any app as the default main section or even have an activity stream/feed based page if you prefer, and there are also built-in forum options like Q&A style forums where members can up/down vote answers and questions like Stack Overflow.
Sometimes all I need is a modern, feature rich gallery and Invision's Core app (which handles registration, members, tasks, user profiles, moderation and admin dashboards etc) combined with the Gallery app is a great alternative to outdated solutions like Coppermine. The flexibility is good, you can always add forums later for example.
Hope this helps, good luck with your search.