You will need a D flute, which is the standard key for playing Irish traditional music.
Wood or polymer?
African Blackwood is generally the wood of choice for Irish flutes, although, as it is now endangered, some makers have instruments in alternative woods. Black in colour, heavy & dense, it is durable and has an excellent sound. Rosewood is lighter and in general cheaper than blackwood.
Polymer can be an excellent alternative to wood, especially for the beginner. It is extremely stable and needs practically no maintenance. In my opinion, a good polymer flute equals a wooden instrument.
To give an idea of price, you can expect to pay from 500 – 700 euros for a wooden instrument, and from 300 – 400 for a polymer. Of course, this is just an indication and prices can vary.
Cheap wooden flutes can sometimes be found on the web, at less than 100 euros; in general these instruments are to be avoided.
Some makers such as Tony Dixon make cylindrical-bore “practice” flutes at less than 100 euros. These are interesting for the beginner on a budget, but are not meant to replace a “real” flute.
Tuneable / non-tuneable
Most flutes will have a tuning slide in the head, which is very useful when you want to play in a group or session. Flutes without tuning slides can be cheaper but, in my opinion, you will eventually need to progress to a tuneable flute.
Keyed or unkeyed?
With an unkeyed Irish flute, you can play in the keays of D and G (and related) which covers the majority of Irish music. In my opinion, keys are not necessary for the beginner or improver.
If you wish to play other traditional or folk musics, keys may be useful. In this case, you can expect to pay (around!) 100 euros+ per key.
There are two main models of Irish flute, both copies of 19th century English flutes. Without trying to give a detailed analysis, here is a brief outline of their characteristics:
The Rudall or Rudall & Rose is a large-bored flute with fairly large holes. The sound is strong and warm, and the instrument is fairly versatile. A Rudall will have a moderate air demand.
The Pratten has a very large bore and large holes. The sound is very strong, powerful and stable. Air demand is a bit more than the Rudall. The reach between the holes may be difficult do master, especially if you have smaller hands.