Hi TlDR: looking for recommendations on mostly flat 2.2 mile city commute using a bike at under £300 or a little over with little to no maintenance.

I am looking for a decent bike that I can use to travel to work. My budget is £300. I do not want to spend too much on it considering distance, its mainly time and energy saver to walking. I would prefer something with little maintenance.

I read a thread where this was recommend however I do not want to take an opinion of a single person so I thought I'd ask. https://www.wiggle.co.uk/brand-x-road-bike

I do not want to buy a second hand, I am not knowledgeable enough about them to know when i strike gold and majority are badly maintained. People sell them for some pocket change. I tried that and it broke down mid travel and I had to walk it to work and back.

The travel distance is 2.2 miles so 4.2 miles total, home and back. The commute is in a city mostly flat with occasional roads going up. My main worries are 2 highway bridges that have spiral slopes, so they seem quite difficult for bikes as they are steep.

So far I think something like a road bike would suit me best as I want to save time and love high speeds. But at same time I hear it takes more maintained which in turn costs more money. I'm a bit hesitant as it makes me think that it would struggle uphill and I would have to pedal really hard or just get off.

Thanks in advance