From the list I wouldn't think you'd go far wrong with the continental double fighters, but I wouldn't go chasing tyres just yet (although they do make a real difference they are not imperative). Getting the bike to work properly is far more important for both your confidence and how your commute feels.
As for the bike, it's your bike, it has two wheels, pedals saddle handlebars, brakes just the same as most other bikes. There should be no reason for the bike not to do you perfectly well enough for the commute you have, but it needs properly setting up and I would suggest that this is where Halfords have to deliver.
How long have you had the bike, as it appears from what you have said through your other threads that the bike has not been sold to you in a state that is fit for purpose and it is their responsibility to fix it or provide you with a replacement or refund.
I would suggest you go back to them and point out that the bike is not fit for purpose, and you demand that it be made so. They make a point about their setup of the bike: -
Don't forget all bikes purchased from Halfords include build, safety check and 6 week first service free of charge.
Make them work for it!
Oh and don't let this experience put you off cycling. Halfords are IMHO unfortunately both, through their big high st stores, one of the greatest enablers of cycling to people new to bikes, and due to their bad setup one of the reasons many people give up cycling. You don't need the shinyest carbon bike in the shop, if the bike works properly then it should be perfectly capable of getting you where you need to go (and it does get a bit easier as your body becomes more used to it). Just think about how enjoyable riding the bike in the summer sunshine will be.
Every time you get annoyed with your bike as it grates away, just think how much money you would have had to spend to get the same workout in a gym
