Before you ride, give your bike a safety check. Its been sitting about for a while, and there could be problems you're not aware of.
The Sustrans website covers this at https://www.sustrans.org.uk/what-you-can-do/cycling/your-bike/bicycle-maintenance-made-easy/m-check-your-bike-11-steps
For things to buy/find:
Wet weather gear - You mention Halfords so its likely you're in the UK, which seems to be enjoying a riding renaissance. But the weather's going to be wet someday. You'll need a coat that works for wet riding. Later you can add overtrousers or overshoes. Personally I ride in gumboots (wellingtons) in the wet.
Helmet - Not mandatory in the UK, but still a very good idea.
Lights - again if your job hours mean riding after dark, lights are probably mandatory for you.
Spare clothes, towel, deodorant. Either carry them with you in a waterproof bag/rack, or store them at work for a change on arrival. Consider using your non-bike days to carry that bag to/from work for starters.
Bike security. Its no good coming out of work and finding your bike's missing. Even though its a cheap BSO bike, a lock will help prevent it from vanishing. I've got access to a bike room at work - check with your MAMIL about where to park it safely.
Water bottle and bottle cage on the bike. On a hot day you can go through a lot of water, so its easier to carry that on the bike and not on your person. Your bike should have a couple of screw holes on the downtube, and a cheap plastic bottle cage will bolt in there with M5 screws. Use grease. Any convenient sized bottle will do, but poptops work best if you drink on the go. Screw tops require you to stop for a sip.
Those are all I'd call immediate needs, and its likely you have a lot of it already (how many people in the UK don't have a waterproof jacket already ?)
If you're handy you would consider carrying pump/spare tube/levers and whatever you need to get the wheel off, for changing a flat. You will get a puncture eventually. Its just a part of cycling.
Depending on how old your bike is, it might benefit from new brake pads. They dry and harden with age, and braking suffers.
If your bike has knobbly MTB tyres, consider replacing them with smoother ones when they wear thin and punctures start getting frequent, or you see canvas.
Otherwise simply keep riding. Aim to wear your bike out and then reward yourself with a better one in a couple years.
Related - recording your rides can be of massive value over time, to see how you're getting faster. Personally I use strava to record my commutes and rides for future comparison. Downside of this, your MAMIL might do so as well, and it may become competitive. Don't be put off if this happens, just use strava to record your own progress and don't compare with other people.
Seeing improvement over time is an awesome ego boost, because it never feels faster at the time.