Oh and I never heard of Bitex.ie.. so I can't recommend for or against it.
Personally I wouldn't use anything which isn't well known and has not a big user base and a great track record.
Bitcove.ie seems to be too expensive on top of that, so I wouldn't use that either way.

If you need someone to sell you Bitcoin (on a regular base,) I could do that for the BitcoinAverage exchange rate (+ a 2% fee).
(https://bitcoinaverage.com/#EUR). But only if you can make deposits to a bankaccount. (Just send me a pm if you are interested in that.)

If you prefer to trade on an exchange yourself, there are many, many exchanges out there. Just try some and stick with the one you like the best. Of course there is always the risk that an exchange gets hacked and/or goes bankrupt.

Another option for you might be LocalBitcoins https://localbitcoins.com/.

And there is of Bitsquare, a decentralized Bitcoin exchange https://bitsquare.io/ (still in beta I think, worth to check it out).