I was in an almost identical position several years ago. The only
difference is we had no heating system in the first place. I looked
into doing it all myself, but in the end decided to do just the wet
work and employ a CORGI guy to install the boiler including all gas
pipes. This I think worked really well and is the approach I wold
recommend.

Learning to plumb is an invaluable skill and will save you thousands
over the years - I know people as young as I employing others to
install washing machines! Whilst getting the plumbing wrong, the worst
that will happen is a leak which can be dealt with easily. The first
few soldered joints certainly weren't perfect. Getting gas wrong
however is a bigger risk and one I saw no reason to take. By doing the
wet work yourself you will be saving on the cost of the time-consuming
labour of that installation - more often that not, the gas work is
quicker and easier.

Also don't bother with courses. Do lots of research online, get the
tools and equipment and have a go. You may end up re-doing much of the
early work once you become competent but the pleasure of knowing you
did it yourself is worth it!

Good luck and let us know how you get on.