You will have to spend several thousand dollars for all that equipment,I have everything you mentioned and I would never purchase one machine that "does it all" you just don't get the quality nor the performance from those types of machines.
If you are just a weekend welder try this for a tig welder,it is %20 duty cycle which is about all you will need for weekend projects and it will also weld aluminum
miller econotig items - Get great deals on Business Industrial, miller diversion items on eBay.com!
Here is a reasonable plasma cutter that will suit your needs
ForceCut LP-40D | Plasma Cutter.
You will need 220v power supply to your shop plus a decent air compressor
With all this equipment you mat as well open up a business sand make money with it, cause it sure wont pay for itself just making bicycle parts.
Good luck on your quest for tools, another option is check craigslist often, there are a few deals on used equipment.