Immortality is essentially a question of understanding a collection of cells well enough to transfer their state to a more robust medium. Performing experiments

Immortality is essentially a question of understanding a collection of cells well enough to transfer their state to a more robust medium. Performing experiments on cells is relatively cheap, and medical research is generally very well funded. On the other hand, a viable starship would require a considerable amount of energy. We'd need to be comfortable travelling within our own solar system, because we're not going to get the amount of energy required from Earth. The best option so far is probably to park some 100km wide solar panels close to the Sun, store up energy for a year, and then use some rather large laser beams to convert that energy into a million ton blackhole. We'd then have a portable generator powerful enough to get us to another star. So my guess is that we'll figure our immortality long before we can seriously think about building a starship.