First thing would be to read up on the types of savings. As defined by the best buys thread there are broadly three, lump sum, fixed term and regular savings.
Based on the title of your thread and the mention of saving an amount of money per month you want a regular saver account. This means you save X euro each month and get interest accrued monthly (usually). These accounts have varying rules e.g. limit of 1000 euro deposit per month, minimum 12 months etc. There may also be limits on withdrawls.
Currently the best rate (as in best buys section) is the EBS Family Saver (which despite its name has nothing to do with family). I recently opened one of these without any bother.
The 10 year solidarity bonds are as the name implies, meant for ten years. This account is different from regular savers in that its not meant for month to month depositing, they are for long term with lump sums, usually providing better interest rates due to the long term and often restrictions on withdrawls. I believe this account is exempt from DIRT also (http://www.statesavings.ie/products/Pages/NationalSolidarityBond.aspx)
However, based on the info you provide,
Best Buy Regular Savers is what youre after
EDIT: also check out
http://compare.nca.ie/ for simple comparison tools on regular savers and lump sum deposit accounts
Hope this helps