Good question. Problem is that there are a lot of answers out there, and it is up to you to pick one.
I was in a similar position 10+ years ago, but with a budget of £500. I didn't really know what I was letting myself in for, and if I had known, I might have made a different choice. But you can't look into the future, and I am happy with the decision that I made.
Firstly, my journey:
I bought a Specialized Allez with 2300 gears, probably equivalent to Claris of the current range. I wanted a bike for high speed commuting, i.e. to beat the time it would take me by car. Distance was 6 miles across the city.
10 years later the bike has taken me through the worst of the winters, and on several 100+ mile sportives over some of the toughest climbs in England. I have changed the wheels a couple of times, cassettes and chains even more, and the whole groupset (upgraded to 105) a couple of years ago. This shows the value of buying a good frame if you aren't the sort of person that needs a new bike every year or two. It has been supplemented with a more robust winter commuter (hub gears, disc brakes) for a good few years now, but is still, by far, my preferred steed.
My recommendations:
Disc brakes, definately, if this is your commuting vehicle. The security of stopping quickly regardless of the weather is invaluable. A road bike with dropped handelbars and road tyres is essential if you are doing 9 miles each way. Anything heavy or suspended will be a drag after the first 5 miles, and will cause you to curse your decision and hate the bike.
Good value bikes inlcude the Boardman range from
Halfords, Pinnacle bikes from
Evans, Planet X, Ribble. Don't ignore Giant or Specialized either. No one ever got laughed at for buying one of those. Declatholon do some superb bikes for the price too. The Triban fits your requirements perfectly.
In terms of bike types, Cyclocross bikes and Gravel bikes have clearances for wider tyres, but that is only necessary for rutted paths or across grass. On roads, a standard frame should be fine.
Have a look, have a dream, and if necessary, come back here for advice.