Chilly spring rides / commuting

Want to start riding earlier this year, I was looking for a suggestion for either a jacket or a jersey for those early spring rides. Here it will be around 40F in the morning and going up to high 50s or low 60s mid day when I begin to ride, temps can range widely and be very cool well into May . Should I have both jersey and jacket? I suppose I could wear my skiing base layer and just get a jacket.

Also to keep my head warm do you wear a beanie under the helmet, or a helmet cover over?

Thanks in advance.

Regards