If you are available for and seeking full-time work, you can sign for Jobseeker's Benefit (if you've been working full time for a few years, you'll probably have enough PRSI contributions to qualify). Your maintenance will not affect this payment if you qualify.
You can apply for One Parent Family Payment(OFP), which is means-tested, but there are some disregards for maintenance, so it won't all be assessed against you. If you qualify for OFP, you can continue to receive half of your Jobseeker's Benefit until your Benefit runs out.
You can apply for Rent Supplement, which is also a means-tested payment, although again, not all of the maintenance will be assessed against you.
If you have savings (from your redundancy, for example), that will be assessed for both OFP and Rent Supplement.
Apply for Jobseeker's and OFP at your nearest Social Welfare Local Office (see
www.welfare.ie for info and you can download some application forms too).
Apply for Rent Supplement from the Community Welfare Officer who is based at your local HSE health centre. While at the health centre, ask about applying for a medical card.