Hello,
If your planning a trip to Ireland in March try to make it during St.Patrick's day on 17th as this is the national holiday. In fact it's more than just 1 day celebration and more a week festival with lots of events organised in every city and town so there will be lots going on.
Just keep in mind that flights and accommodation can be very expensive at this time of year as half the people in the world are Irish and the other half want to be at this time and all seem to converge on the island on that day.
http://www.stpatricksfestival.ie/
As for the weather, don't worry about it too much.
In March you should expect glorious warm sunshine followed by a snow blizzard. In otherwords, be prepared for all types of weather and you won't be disappointed. Like in switzerland, hope for the best but prepare for the worst.
If you just have a week to spend in ireland then split your time between Dublin and the countryside.
Maybe 2 or 3 nights in Dublin city depending on what you want to see and do.
Here are some recommendations from my experience before I left my home town for Zurich. My wife being French meant I had to be a part time tour guide every time her family and friends arrived for a holiday.
Guinness storehouse
Original brewery, and ireland's number 1 tourist destination, for Guinness.
7 floors giving a visiter a history lesson on Guinness and Dublin. Finishing on the top floor with a bar and free Pint. Don't worry if you don't like the taste. Just do like most tourists and take a picture holding the glass. There is a glass wall around the bar giving a 360° view of Dublin.
http://www.guinness-storehouse.com/en/Index.aspx
Christ Church Cathedral
Right in the city is Christ Church cathedral which is open to visitors and is a wonderful place to visit during the day. You should also include a visit to the crypt (like a museum) under the church and the viking museum next door which is connected to the cathedral.
http://www.christchurchdublin.ie/
http://www.dublinia.ie/
While in that area you can join the Viking splash tour.
This involves taking a bus journey around Dublin with a special twist. The bus is also a boat and enters the River Liffey during the tour to bring you on a journey along the river.
Oh and you also have to dress up as a viking and shout at all the people on the street. Not just for kids and I've brought plenty of my wife's friends on this trip and they've loved it.
http://www.vikingsplash.com/
But if you like a beer or just generally having a good time then you will not be bored in Dublin. It's famous for pubs and has plenty of niteclubs too if you have the stamina. temple Bar is the main area for the party goers and has plenty of pubs and lots of stag and hen parties too especially at the weekend.
http://www.templebar.ie/
But by no means spend too long in that area. Dublin is full of terrific bars and pubs, many of which serve good food too and you can often hear live Irish music in many of them too if that is what you like.
But if heading to the countryside it's best to go by car from Dublin.
Everyone has a different opinion as to what they like on a holiday but personally I feel best places to visit outside Dublin within your week include
Kilkenny City
Old medieval city with one of the most impressive castles in Ireland in the centre of the city. The official tour is excellent and should certainly be on your list.
http://www.kilkennycastle.ie/en/
In the south west is Killarney.
This is probably the most impressive part of Ireland for scenery and with the car you can take a beautiful scenic drive around the area with incredible views of the Atlantic ocean. Well worth staying there for 1 or 2 days.
http://www.killarney.ie/
In the west directly across from Dublin is Galway city and the Aran Islands.
Again an area that has spectacular scenery and the city itself has lots to offer visitors especially if you like water sports.
http://www.galwaytourism.ie/
This is just a small amount of lots of things you can do in Ireland. But it's just my opinion and it's all about what interests you. But I think there is something there to interest everyone.
If you need anymore more information I would be happy to help.
But most of all enjoy the trip and have fun!
John