First off, it will be very useful to have some hardware knowledge before you start. Transfering matlab algorithms to FPGAs starts in matlab, by having someone experienced in FPGAs help re-design it from a hardware approach. Some simple concepts in C/MATLAB can be really difficult and expensive to implement on an FPGA when some simple architectural changes can make all the difference.
Ive not used any C to HDL tools, but anything I have read/heard seems to point to poor performing implementations that can work, but not very or efficiently.
As for HDL coder, I have used it. My opinion is that it is best suited to simple pipelined algorithms. Anything that needs a detailed level of control is best hand coded. Its great for arithmatic but not great for control logic. Again, others experience is that its great for architecting and prototyping a system, but not great for final implementation. What it is amazing for is modelling and verification. I have much love for simulink-modelsim co-simulation.
The only downside is that none of these tools are free. Quartus is basically just a code compiler (compiling HDLs), and there are no translation tools. All of these have to be bought and come at considerable cost (I think an HDL coder licence is around $10k per seat!).
So my advice is to learn up about digital hardware design as a first step. Or get someone in who is.