You will hear some people tell you to start with a .22, and others tell you to start with something else.
The key is to start with something you feel comfortable with.
My first handgun was a .40 and that was fine by me, but then again I was educated in the realm of firearms before I purchased it.
If I were you, and I went and took the NRA-approved day-long pistol training/safety course, I'd be willing to bet that you would be more than comfortable owning a 9, 40, or even larger as your first firearm.
Will and I spent a couple times at the range, and maybe an hour total time going over safety and how things work instruction, before he went and bought his first firearm; A Ruger P94 9mm, and it suits him just fine.
I highly recommend the HK, and I hate Glocks, but I'm biased -- and admittingly, both are great guns.
What I recommend is go take the course, then spend a couple bux at ranges renting different types of firearms (I recommend trying a Glock, Beretta, Sig, HK and Ruger) of all different caliburs (9, 45, 40 -- though I presume you'll end up with a 9 or 40) and decide what fits your hand what you are most comfortable with.
Then you get the neat decision of developing a cost base -- what you want to spend and how often you want to shoot.
For instance .22 ammunition is like $10 for 500 rounds; 9mm is like $12 for 100, and .40 is about $15 for 100. So ammunition gets more expensive as you stray from small to larger rounds -- but on the other hand, they're more capable and better rounds.
Like I said, first steps first. Take the course, and go spend a couple hours at various ranges trying multiple handguns and deciding what fits your hand best -- and then you can worry about what you want to spend and what suits your needs.
(My gut feel says you're going to end up with a Glock -- because they're relatively low cost, low maintenence, easy to shoot, and accurate -- but I'd choose an HK or SIG over the Glock anyday)