Started my running log in 1977, will be finishing 43 years in about two weeks. I've always used green or buff Engineering paper, one sheet for first half of month, one sheet for second half. I line it off with two lines per day, and have four columns lined off on each sheet. Use felt tip pens that don't fade (mostly Flair). For races, I note the short details on the date, then just use a sheet of loose leaf paper for race details. More loose leaf paper for shoes purchased over the years, another page for PR's (sadly none since 1991). Then put five years of the daily pages in a loose leaf binder. A smaller ring binder that just records daily mileage and totals. Sounds complicated but it's really nothing, much easier than inputting into a spreadsheet or database. Every few months, I scan my pages into the computer and do a backup on that, just in case.
One of the things that I've noticed over the years is that when I look at my handwriting in my logs, I can get a sense of how things were going then by the handwriting itself. Can't get that same feeling in a spreadsheet. I guess there is some emotion of something in the writing, who knows.
I've got nothing against Strava or any of the other online services, but if they decide to shut down or something, there is a good chance that all your logs will go with them. I learned that lesson when Geocities shut down. Don't be dependent (if possible) on trusting someone else to safeguard your info.