Part of this can be answered by asking the question: “Where are you looking for a guild?” Sadly, the in-game guild finder isn’t fabulous and using other sources is a far better way to find guilds.
However… STEP ONE is to prepare yourself for a guild. This means asking yourself what are you looking for in a guild? Thinking about not just activities, but also about culture fit. Do you want a guild super active in Discord or more active in /g chat? Are you hoping for a guild with perks like an allowance for repairs or maybe one which has class leads off of which you can bounce ideas and questions? Does your preferred humor lean more towards NSFW or more towards family-friendly? (Culture fit is EASILY the hardest part!!!) At the same time you want to honestly assess your own ability and available times (including amount of time) you have to play.
The “why” for all that is super simple… if you want to focus on M+, you’re not going to be happy in a guild which is focused on raids. If you want to raid, a guild heavy into PvP won’t be your thing. Or maybe you can only play in the evenings in eastern time zone and thus wouldn’t be happy in a guild mostly active during west coast evening hours. You yourself brought up how it can be hard to have significantly different ability from your guild, so you already see that angle. Etc, etc, etc…
Once you have done that above homework, the hard part starts, which is actually hunting down a guild which fits what you’re looking for and NOT just joining, but talking to them first. AND YOU WILL TALK TO A LOT OF PEOPLE IN SEARCH OF THE RIGHT GUILD… LOTS… OF… PEOPLE. Honestly, no really amazing guild is going to just toss invites out left/right. They’re amazing because they have built a guild culture their group enjoys and will want to talk to you to make sure you fit that culture before bringing you on board. (At the core, that is THE THING which makes an amazing guild amazing.) Some examples of external places to look for guilds in WoW are Facebook, Reddit, WoWprogress, and RaiderIO. Of course many guilds will also advertise here on the forums and how the posts are written can give you a jump start on the feel of the guild.
Dumb as it sounds, talk in PUGs. Did you just queue into a group of four from the same guild? Chat, if they’re interested to chat back. Even if they aren’t the right guild, they might give you another name. (“Oh, if you want to raid, my friend’s guild raids. He/she loves them!!”) Also, something I can’t stress strongly enough, TAKE NOTES!! Write down the guild name, the name of the guild master or officer with which you’re talking (larger guilds will frequently have an officer in charge of recruiting), jot down the names of other people from the guild you’ve met, what you did with them, and your impressions of them, and jot down the pluses/minuses of the guild.
(Example: “Guild of Greatness”, officer: Soandso, ran some M+ with Hithere who always seemed super high energy, pluses: has a guild raid and offers repairs/flasks, minuses: more active when I’m at work.)
Do not try to just remember it all because you won’t remember. You’ll find yourself thinking “wait, who was it who did/said this/that?”
But the bottom line is, you only find the right guild by getting out there and talking to people. If you want to raid or focus on M+, I recommend PUGing a few raids and recording the logs so you have something to show to your potential new guild. They will have questions for you, but you should also have some for them about things which are important to you!
Lastly, remember this is NOT going to happen overnight. When my group did our guild search it took us easily four months. That was four months of trail running with groups, hanging out with other groups to get a feel for the culture, and involved a lot of having to say: “You guys are a great group, but it just feels like the wrong fit” and parting ways amicably. Don’t settle when it doesn’t feel right. If you settle when something isn’t right, that something is going to start to seem bigger and bigger over time.
BTW, this is coming from someone who belonged to my original guild all the way from vanilla until the guild finally folded mid-BfA. Literally about fourteen years with the same group – several of which I’m still in touch with!! I know what I’m talking about. 
