Some things to consider.
Firstly, Dublin is not a commuter friendly city. Traffic is bad and parking is taxed and discouraged, so driving is not a good option.
If you are working in the Trinity area, then forget about any of the aforementioned train links to Kildare/Naas/Newbridge etc. - Heuston station is too far away from Trinity and there are few direct public transport links between the two.
You best bet is areas along the DART and commuter rail services along the rail line which stops in Pearse and Tara St Stations. This line actually runs through the grounds of Trinity, so you cant get much closer. On the DART line, you have any areas between Malahide/Howth and Greystones. There are areas to suit all tastes and budgets along this line. Trains are every few minutes, so you dont have to rely on timetables.
Going further afield, your other options for commuter routes going through these stations are along the Drogheda commuter rail - this serves north county Dublin which still has a semi-rural feel about it. You could also consider places along the Maynooth line, however this line has a reputation for the trains being overcrowded.
As other posters have said, you'd be better renting for a year or so to give yourself time to get to know the city and be able to make a decision on what areas you would like to live permanently.
On you finances. You mention that your budget is c.250k. You have different mortgage rates/currency in Ireland to UK, so it would be better for you to set your budget as "we can afford to spend €??? per month on rent/mortgage" and chose properties where the rent/repayments are within this budget rather than looking at things in pure capital spend terms.
I hope you enjoy living in Ireland - English people are always made very welcome in Dublin and find it easy to assimilate (I know some who've made the move already). In spite of all the media hype about recessions, you'll still find that wages are generally higher and direct taxes generally lower than the UK and the standard of living is still slightly ahead of the UK.