I would look at business class rather than first, most airlines will operate a business class product TATL but fewer operate first in addition.

You have a few options:
- Cash ticket up front in business or first. Guaranteed seat/class/date.
- Wait for a published sale in business or first.
- Hope for a mistake fare at a large discount, low probability
- Book an award ticket with miles will be cheaper depending on availability, to earn the miles you can either open credit cards, fly to earn, buy the miles, etc
- Upgrade from a lower class with miles/cash, depends on the airline you are flying whether you can do this, whether it is guaranteed or not and how it is done

Another thing to keep in mind is that unless you can get a direct flight, you will likely have at least one connecting flight.

European shorthaul airlines business class is generally the same seating as economy, but with a middle seat blocked, a curtain divider and slightly better service.