Take this in small step but before you even start decide what you want to make. Size under the cutting head + material to be cut + accuracy + repeatability (Note accuracy and repeatability are different and unless you are going to supply parts or use parts made on other machines it is the repeatability that is important not the absolute accuracy.) Then the surface finish and dust or chip control.
Join the club where cash is king!
1. Mach3 runs most of its features from the free download edition. Pay only when you have got your machine running and need the extra features provided by the licensed software or are going into paid work on the machine.
2. Mach3 in not a heavy user of computing power but it requires real time control over the parallel port. (There are some fancy USB and Ethernet adaptors but these cost money and expertise to use.) There is advice on the type of computer on the Mach3 website. Must have Microsoft Windows operating system go for XP or Win 7 although Vista will work if you remove all its party tricks.) You do not need the high performance features so base versions from Microsoft are OK. Best to avoid lap tops as they use peculiar settings that may be difficult to inhibit as they are designed to save power and slow down when lightly used but since most laptops don't have a parallel port anyway that rules them out. I suggest a low specification desk top possibly a cast off as the demands are very low in terms of processor power. The shared use of RAM by the graphics can cause problems so an Intel mother board will be good but not one that uses the S3 graphics chip. The amount of RAM needs to be enough to run Windows + a bit fro running the program so a minimum spec machine is all that is required. It is possible to use a mother board kitted out with Ram and processor + a low capacity hard disk these are often available as a clearance bundle from electronics outlets but by the time you have bought Windows a second hand machine is a very attractive option. And you will need a display VDU or LCD.
3. Look at the Linux CNC software EMC2 as this is free and is well thought of.
4. Calculate or copy and existing known good design for motor size and gantry construction.
Rough out your design and price up parts for alternative drive mechanisms and keep an eye on eBay and any local sources including skips!
Read the many threads on the CNC Zone as it is a good source of both information and help.
Above all have fun as there is much enjoyment to be had but do stay safe as any machine tool can turn nasty when abused. Regards - Pat