What Bit set would you have me put together as a new carver?
What spindle are you using? That makes a big difference. 
Personally, for just starting out, I’d get a 1/8", a 1/16th inch (or several, they break easily) and a 1/4". For fluting, I personally like single or two-flute downshear bits, but two-flute straight or up-shear bits work well also. At the moment, I am primarily using Freud router bits, to be honest, although I have a very nice Onsrud unliflute downshear that I break out when I need a REALLY fine surface on the milled parts.
what would you recommend for cutting through 18mm mdf sheets?
To start I purchased 1/16, 1/8 and 1/4 inch 2 flute endmills (flat bottom for 2D cuts) and ball nose (for 3D finish passes) (6 bits in all) and then I purchased 30, 60 and 90 degree vbits for lettering and fine detail carving.
I am partial to a two-flute upspiral 1/4" bit, for that kind of work. Clears chips very well and is rigid enough for goodly-depth passes. I’m using mine currently to cut through 3/4in (19mm) cherry in three passes (about 7mm per pass) at 50 in/min (127cm/min), and it has no trouble at all. I’m using the DeWalt 611 as my spindle, and could probably make that cut even faster if I really needed to. In MDF, it would do it in two fairly easily, I think.