As a general principle, you should not be tying up your money in long term products such as the NTMA. You have a plan at the moment to stay where you are for a few years and then return. But plans change quickly. If you decide you want to buy a house in Ireland, or even in the UK, you will be caught out badly by your NTMA investment. I presume you can cash it, but the interest rate you get will be poor.
The correct long term investment is to buy your home. When you buy it, you want to have as big a deposit as possible so that you will benefit from the lower mortgage rates which attach to lower Loan to Value mortgages. So all your money should be easily accessible at short notice.
If your plan is to return to Ireland at some stage, you should probably not buy a house in the UK. There are advantages in being a First Time Buyer, and you would lose that status by buying in the UK.
As you seem to have an investment horizon of a few years, I think you should invest in the equity market. Of course, the risk is that when you are ready to buy a house, the value of your investment might be lower. But this risk reduces the longer you hold the shares. And the risk/reward is better than any other investment.
As a non-dom in the UK, you probably have options to invest overseas quite tax efficiently.
Having said that, ISAs and direct holding of shares in the UK seem quite tax efficient as well.
Brendan