Which pad, in one line each
Android phone, lowest price, longest life. 8BitDo Pro 2. Its listing names Android, macOS, Windows, Steam, Switch and Switch 2, and it carries Hall effect sticks. The catch is the layout: it is a Super Nintendo-style pad with grips, so the face buttons are not where an Xbox-trained thumb expects them.
iPhone. 8BitDo Ultimate 2, which is the one here listed for Apple as well as PC, Steam and Android, in a conventional modern layout. Note that unlike the Pro 2 it is not listed for Nintendo Switch, so if you want one pad for a phone and a Switch, buy the Pro 2 instead.
You already own an Xbox. The Xbox Wireless Controller, whose listing covers Xbox consoles, PCs, TVs and mobile over Bluetooth and USB-C. Every game that draws button prompts draws the right ones. It still runs on AA batteries out of the box, which is the running cost the others do not have.
You already own a PS5. The DualSense, listed for PS5, PC, Mac and mobile. It is rechargeable and it is the pad a PS5 household already has a spare of - the one caveat being that its adaptive triggers and haptics are a PS5 feature and do not follow it onto a phone.
Which game, by what you want from the evening
Build something with friends. Minecraft. Phones, PS5, Xbox, PC and Switch with Bedrock crossplay across all of them, and one to eight-plus players online or local - which makes it the only pick here where the phone player is a full participant in a group that is otherwise on consoles. The full review covers the edition question, which is the thing most groups get wrong.
A big single-player world you occasionally share. Genshin Impact. Free, one to four in online co-op, crossplay and cross-save across PS5, PC and mobile, so the same account moves between a phone on the train and a console at home.
Two of you, something long.Terraria or Stardew Valley. Terraria runs one to eight in co-op and crossplays across most platforms on the same version; Stardew Valley is one to four and is same-platform only, which matters if the two of you are on different phones' ecosystems - see games like Stardew Valley for the alternatives if that rules it out.
Physics comedy with a group. Human: Fall Flat. One to eight, online and local, crossplay across platforms, and it is usually the cheapest paid game on any list it appears on. A pad helps here more than almost anywhere, because the entire game is analogue arm control.
Free, and with a squad. Fortnite for up to four in a squad with full crossplay to every platform, or Warframe for one to four in co-op with cross-platform play and Cross Save everywhere. Both are free, so a pad is the only money involved.
Where to go next
The main mobile list is the page to read if you have not decided on a game yet, and free mobile games is the version with nothing to buy. If the controller is really for a television rather than a phone, the second controller guide ranks the same pads for couch co-op and the couch gaming setup covers getting a PC onto the big screen. And if the group is mixed between phones and consoles, phone and console crossplay is the list of games that genuinely bridge the two.