Headphones for daily use but for under £200...

Seasons greetings!

Apologies that my first post is a plea for advice.

I am looking to buy some new headphones over the next few weeks, and I am very new to the audiophile headphone market.
I assumed naively that buying a pair of headphones for under £200 would be a matter of seeing which pair had the most favourable reviews online, and then finding the cheapest place to buy these cans. The more I researched, the more factors I realised I had to take into account, and the more confused I became. My confusion was not helped by the fact that none of the shops in my area allow you to try out headphones, and I found it difficult to trust their advice. 'Beats are the best on the market!' was a line I got sick of hearing. (If there is one conclusion my research allowed me to make, it was that I was not going to buy 'Beats' Headphones)

The factors which clouded the issue for me were:

The existence of Ohm values - I noticed that some models were made identical except for this value (The DT880's spring to mind)

Headphone amplifiers - I gathered that the need for these depended at least partly on the Ohm value, but am completely in the dark as to the conditions which warrant their use, and the portion of my budget I should set aside for these

Closed/open back - I was literally heartbroken when I found that the HD 598's would be impossible to use on public transport due to the sheer amount of sound that they leak. Not only do they seem to receive excellent reviews, but they are also the most beautiful things I have clasped eyes on...

To cut to the chase, I am looking to spend £200 on a pair of headphones (and headphone amplifier if required) which sound stunning playing a range of music (anything from metal through to classical, drum and bass, country...etc) and which will be suitable for use on public transport

Thanks in advance for any advice.