You can do what you want with a 3-axis solution, no question. It could possibly be done with a singe 1/8" ball end mill, but I would suggest a 1/4" roughing mill first, then a nice slow final pass with the ball end.
You could be up and running, including ALL the required drives and motors, for $1200 with a Fireball V90 from Probotix. This will probably be your "cheapest" way to test if this is a path you want to go. It could last you months, or you may outgrow it quickly, but the skills you learn on it will be 100% transferable to whatever you may want to step up to. Downside: The machine is made of MDF. Before you laugh to loud, this isn't all bad, and for cutting wood knife handles, it is more than up to the job.
See here:
http://www.probotix.com/FireBall_v90_cnc_router_kit/
E-mail Len if you have any questions.
Once you have this, or any other system, up and running, you need to tackle the rest of the steps in the chain. You will need to take your CAD models in to a CAM package. These run from free to $20k+. I use BobCAD, and I find it suitable for my needs. You can get what you need for $600 (it will likely list for $2000-3000, but they are pretty easy to talk down - don't give them your real phone number, and hang up if you don't get the deal you want).
So, your CAM package will change your CAD model in to GCode, which is what the CNC needs to run. So your next step is to choose the software to drive the machine. If you know Linux, I would suggest EMC2, as it is fully featured, and it is free. If you don't know Linux, I would avoid adding it to your list of things to learn, and buy a seat of MACH3 for less than $200. This is also full featured, and runs in Windows (you will need a parallel port for the most economical way to run it).
So, finally, you will want a computer that is dedicated to the CNC. This can be any old Desktop machine, 1 GHz or higher should be fine (even a Pentium 4). It should have Win95 or newer - you do NOT need a new computer! Actually, many new computers no longer have a parallel port, so you will be best off with something 2-4 years old.
You have a pretty big hill ahead of you, but you can scale it! Getting a machine is only one step in your upcoming learning process, so take the advice you get, and make informed decisions as much as possible.
Ditch the whole idea of 4th or 5th axis, this is WAY overkill for what you want to do, and is MUCH more expensive than the posts above would seem to indicate (the software to create true 4th and 5th axis code starts at $10k except for one open source program out there that is WAY difficult to learn).
So, you can get to your end goal for under $3000 "all in", but there are more pieces to the puzzle than you have indicated concern for so far. The sky is the limit on how much you "can" spend on a useable setup, so set a budget, and weigh what you "want" versus what you "need"!
Best of luck!
In the mean time, if you want me to cut some parts for you, e-mail me at
[email protected]. I'd be happy to turn your IGES files in to real parts for "much less" than traditional machine shops are likely charging you. If you want a sample of the output a V90 could provide you, send one of your files to the e-mail above, and I can cut one out of some 2x4 stock for you to take a look.