A full block gets about .2 btc in fees, so roughly .2 btc / 1MB of space. The human genome is allegedly somewhere between 1.5GB - 2.0GB of ATGC data.
Now there is going to be some extra space needed, because as you try to stuff your dna in the blockchain there is going to be other transactions inbetween. So you're going to need to put pointers to where your last data segment was so that you can reconstruct your genome in the future. But we're going to ignore all that overhead and get a lower bound of the price.
2,000MB * .2 btc / MB ~= 400 btc
Immortality isn't cheap!