Is it OK to wait until I get there (Basel) to plan day trips by train, or is there a big difference in price and availability if I book right now from home?
Are you considering the Swiss Travel Pass?
Check out the postings under the Switzerland section here on the Forum for a vast amount of info regarding travel within Switzerland.
Safe travels!
day trips won't be far, no matter if you visit close places in Switzerland, or France or Germany (Basel as you will know is at the triple meeting point) and regional trains will be frequent and reasonably inexpensive.
Easy to get immediately before travel...
Agree with Nigel. Pay as you go on the local trains. You have lots of daytrip options from Basel.