A digital dive log is the way to go. Preferrably one that has a mobile app so you've got the dives available on your phone, in the off chance that you'd need to produce them, or more likely, you want to check a gear/weight configuration at a later date, or if you can't recall if you were cold in that 82 degree water with a 3/2 skin, that sort of thing.
Even better is one that allows you to hook your dive computer to a PC and upload data including date, time, depth, bottom time, and additional information such as SAC rates which are automatically calculated by most air integrated computers. The data builds and travels with you as you progress through your dive career and can make diving safer and more fun.
Don't use a log that is entirely website based because if goes defunct and you can't download your data you're going to either lose it or have a lot of work to do in order to rebuild it elsewhere. Diverrecord.com is one such example.
I use Subsurface- it has all these features, is easy to use, and best of all it's free. It has a local and cloud based storage so you're not dependent on them for your data. You can import and export your dive data if needed, for another application.
P.S. You should log your OW checkout dives, including the weights you used, the temperature of the water if you know it or can retrieve it from your dive computer should you happen to own one, and any notable things about the dive itself that might be worth reviewing at a later date.
most training dives still need to be logged and stamped by an instructor or dive centre..
That's news to me.
