The only advantage whatsoever that I've noticed with jerseys (and I have a very high quality one) is the rear-facing pockets that you don't find on any other type of clothing. It's remarkable how reliable those pockets are - despite seeming like you'd lose change, keys, etc., I've yet to lose a single item - even after going down 3 times on my bike. I even carried 2 water bottles back there for awhile when I was doing regular 4+ hr rides on the weekends and didn't want to add a rear rack to my aero framed bike and I didn't even notice them.
Aside from the pockets, though, it's the same exact material as running shirts - polyester/lycra blends. Running shirts work perfectly well, and if they're tighter, they're more aero and will actually work better than a loose fitting cycling jersey. I sporadically put on my 'fred' running gear outfit from time to time to match my fredly entry level road bike, and then hammer the hillclimb with the local competitive roadie crews and it's always funny how I get a bunch of 'good jobs!' (I take it at they expected me to be a beginner noob) at the end whereas if I wear my Cervelo kit, nobody gives a ### because they expect you to ride fast.
I don't think cycling socks are worth it at all - I don't even notice them after 2 minutes in the shoes, but I also have never gotten blisters riding.
The clothing that I think is actually very useful and bike-specific:
- Bike shorts. If you're riding over an hour, you should invest in these, as your butt will get rubbed raw with loose clothing down there. You don't need the best, but you definitely shouldn't skimp on these - there's a very big difference betwen $30 shorts and $80-100 shorts. Thicker pads also do not mean better - a lot has to do with how snug the fit is on you without being constricting.
- Windproof shell for cooler days. You can wear one of these in temps from 30F to 80F and be more or less ok if you wear a baselayer if it's <55. Wind chill can be rough on a bike.
- If you're riding in cold areas, booties or at least toe covers. I used to think those things were excessive, until I rode in LA in a 48F day (not bad at all for riding) into a bunch of dark canyons in the Santa monica mts where temps dropped to mid30s. My upper body was warm, but I nearly got frostbite in my toes due to the extreme cold from wind chill -had to bail the ride early as a result. Ever since, I've been diligent about wearing the booties on cold days.
I routinely do 90-120 minute solo bike rides at a moderate pace wearing a running top, as I don't need the pocket storage, and I like how my compression running shirt fits. I often wear that same shirt as a baselayer under a windproof jacket for cold days. I've been very underwhelmed with my bike jersey compared with cheapo running poly shirts that fit snugly.