All of the current models of Macs are very speedy.
Typing and browsing and typical planning are lightweight. Games can push hardware a little harder.
If you have specific apps that you plan to use, check which have system recommendations, and what those recommendations are. e.g. Microsoft 365 apps, Adobe Creative Cloud, that game, etc.
At its simplest, you get to choose whether you want portability and lower-end prices (Air) or want higher-end features and higher-end costs (Pro).
https://www.apple.com/mac/compare/?modelList=MacBook-Air-M2,MacBook-Pro-16-M3,MacBook-Pro-14-M3
Whatever you pick, I wouldn’t go below 16 GB memory, and more storage than you think you need. Neither of these can be increased over the life of the Mac.
As an alternative approach, an iPad can do all of what you’ve asked for, except for the particular game. You might want to look at an iPad for mobile and a Mac mini or iMac at a desk for instance. Desktops tend to be cheaper than portable computers for equivalent capabilities, so you might even finish at around the same total cost for both.
Budget for a hard disk drive sufficient for your Time Machine backups, too. That’s probably a four- to six-terabyte hard disk, depending on how much internal storage and how deep you want your backups. Or for a NAS, if you have a budget for that, and want wireless backups.