My ha' p 'orth after 45 years of mountaineering and cycling: the best investment you can make is a Helly Hansen Lifa top, that's the very snug fitting polypropylene top which has white stripes on the arms:
This is a versatile and justifiably popular garment you can wear for cycling, running, walking, skiing, any sport where you are likely to sweat. It keeps your insulating mid layer separated from your skin while allowing sweat to pass through. A cotton T shirt will get soaked and feel clammy.
The next best investment would be a pair of Ron Hill Tracksters:
Another excellent and versatile garment, you can wear them over cycling shorts in Spring and Autumn and use them for running, under a shell for skiing, as summer walking breeches rolled up, for general lounging around and even in bed!
Both garments wash and dry easily and quickly and will last you for years.
As a rule, for road riding buy clothes which are snug fitting because you don't want loose flapping fabrics and it looks naff riding along with a big jacket bulging out, as well as catching the wind.
Helmet: having clouted my head very hard on the pavement once is a fast tumbling fall I am never without a helmet as I reckon mine saved me a bad injury or worse.