I find myself in a similar situation when I commute to college on weekends. During sleep you'll get sweaty and our beds are not the most hygienic places in any case so before starting off on your journey, have a shower. If you don't have a shower and you sweat, you'll be combining sweat with dirt etc and this is when body odour will form.
In terms of what you should wear:
- Wind breaker for upper body (personally I use a Castelli Gabba)
- Bib tights for lower body (I'd avoid thermal bibs as you can only wear them when cold, normal bibs you can wear in normal weather or in cold weather with a base layer.
- Base layers for both upper and lower body with good wick
- Warm gloves - My own are not waterproof but I keep a set of surgical gloves in my backpack, if it rains I put them on underneath my existing gloves so I'm kept dry and warm.
- Overshoes - get a waterproof set, this will keep the wind and water out while keeping you warm.
- Balaclava - personally I like the GripGrab balaclava and it can cover just your head or full head coverage plus half face, good to have options.
- Optional - aero helmet - this might seem overkill but I managed to pick up a really nice time trial helmet which has mimimal vents, keeping me a little warmer on my commute. These can run expensive so not a necessity.
As I've nowhere to hang my bicycle gear in college, I will have 2 plastic bags in my backpack for my used gear. 1 is for stuff I won't use again, most of the time this is just socks but on occasions, where I've sweat a little too much I'll put base layers there too. The other is for gear I will use again on my return trip like jacket/tights etc. If my jacket is not particularly smelly (yes it happens) then I'll hang it off my chair in college to let some air at it. By the time I get going in the afternoon/evening, the gear I put back on will be smelly so it gets washed at the end of the day, this is very important from a hygiene and odour perspective.
In terms of cleanup, I will bring odour free baby wipes and will wipe myself down paying particular attention to creases (elbows, groin, behind my knees etc.) in my body. I'll then use a small microfiber towel to fully dry myself.
You mention you're an amateur biker, so am I but if I didn't have the gear above I probably wouldn't even feel like going cycling as I'd be too cold/wet when I got going. Always choose the right equipment for the job. Your bicycle gear will be an investment in a healthier you. Organising your bag the night before goes a long way. I get mine done as soon as I'm from my day, so I'm replacing anything I used that day with fresh stuff for the next day.