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Bioinformatics is a very broad field. The rage in bioinformatics right now is genomics, but there's a whole host of other spheres apart from that. There's protein chemistry, biomolecular interactions, organism data metanalysis (finding correlations amongst things like heart rate, metabolism, disease phenotypes, etc), and plenty more.
Think of bioinformatics as "answering questions and solving problems in the life sciences based on data from living things using the computational domain."
Dan is very correct. Being a good bioinformatician means being a biologist who wants to use computational methods to explore biological questions.
Don't become another programmer throwing rocks at biologists from your ivory tower. There's already too many of them.
My suggestion would be to approach your questions from two directions. You should look at the biology available to you and see if anything interests you, from there you can explore what dry methods will allow you to explore those biological questions. The other approach is to look at computational methods that interest you and then back to the biology to find biological problems you can answer with methods you're interested in.
Try as they may, the computational and wet sides of life sciences aren't as loosely coupled as people like to make them. The better you understand life sciences in general and the biology driving the need for computational solutions, the more successful you will be.
Just like we don't need another software package written in the author's pet language, we don't need another algorithm that does the same stuff but in a way the author thinks is cool. Great you wrote a de novo assembler that uses approach x instead of y and gets meager at best improvements? It will go in the pile where it won't be used because a good enough solution already exists.
What you should look for are totally new (but needed) forms of analysis, or ways to leverage high throughput technologies to allow new scales and questions of biology to be explored. The advances that have allowed Maxam-Gilbert sequencing to be replaced with shotgun and sanger sequencing were what allowed the human genome to be sequenced. This type of advance is where bioinformatics really shines and is in general the types of research you should aim for.
Think in terms of advancing biology, not algorithmic efficiency pissing contests. Going back to the assembler example, unless your assembler can assemble a mammalian genome on a smartphone while I'm reading the news, I'm not going to care.Minor improvements in efficiency/performance are going to get you a "just another algorithm" trophy.
Also, like Dan said, bioinformatics isn't just genomics and it especially isn't just human and mouse cancer genomics. There are huge worlds of biology that would benefit from new computational methods. Honestly, I know you're a CS person, but I think taking some time to seriously explore biology would greatly benefit you.
If it is possible, I would highly recommend that you get some decent time in a wet lab doing wet biology, especially if it is the biology you're interested in. My current position has me doing 40/60 wet and dry, and it has been a hugely important experience. It has been humbling to really see the limits of dry biology (of which there are many), and hugely important for me as a scientist and experimentalist.
You don't have to be an expert, that's not what I'm suggesting. I'm simply saying that having a bit of wet experience really helps you understand the processes and limitations on both sides of the biology fence as well as a better understanding of where your data comes from. A bit of "well roundedness" if you will, neither necessary nor sufficient, but it goes a long way.
On the note of biologists-turned-bioinformaticians, you don't need a CS degree to be able to write good code or program in general. Plenty of software (and even "robust and efficient programs") has been written by people who aren't CS by training. I've never understood this sentiment. This has been my personal experience, only 3 courses I took during undergrad were in CS, and mainly because I could take them instead of biology I wasn't interested in. I'm sure I'm not the only one.