What items do I need to do repairs and tune a compound bow.
Also, how much should I expect to spend.

It depends on what you are planning to do. Do you plan on being able to completely take down your bow (changing strings, etc)? Are you going to change servings, tie on things to your strings? Or you you mean, just being able to tune your bow.

If you are planning to tune your bow, all you really need is a good set of allen wrenches. If you are planning on paper tuning, you can build your own (I use a tree stand box with a window cut out on bith sides and tape the shoot through paper on it).

I geuss I' m looking at doing everything.
I want to slowly be able to make all repairs to my bow.
I' m thinking of the basics to start: changing my string, nocks, installing silencing material to the strings, adjusting bow weight(Pull), installing and aligning peep sights, etc..

Then you will need a good bow press ie apple.
allen wrenches, weight scale, string jig (if you want to make your own strings) arrow grain scale, bow square, nocking plyers, serving material, a frame for paper tuning and a few other things that dont readily come to mind at the moment

I think Ausie pretty much covered the important things. If you' re like me & can' t afford to go out & get it all at once, I' d say start with a good set of allen wrenches, nocking pliers and a bow square. You should be able to pick up those items for around $30 or so. Assuming you know about what draw weight your bow was set up at, these items should get you through most everything you need to do to tune your bow. You can always improvise a little when setting something up for paper tuning so you don' t necessarily need to buy a frame right away.

The next thing I would add would be a scale to check your draw weight and the arrow grain scale. You should know about what your draw weight is from the shop that set you up, and you can figure out about what your arrows should weigh by looking up weight of the shaft & components. But being able to check the exact draw weight and the exact weight of each arrow will be helpful at some point. Just off the top of my head, I' d say expect to spend a minimum of $50 -$60 and probably more, depending on the quality.

A good bench top press would be great when it comes time to install a new string. I will have one as soon as I save up a little more cash. I believe they start around $175 or so. I recently replaced my string & cable with one of those $35 portable bow presses. It worked pretty good but it would be nice to have a bench top press that holds the bow for you while you work.

The portable press also worked well for installing my string leeches and peep. But again it would be nice to have a press that held my bow so it would be easier to work on.

Thanks, I' ll start shopping Cabela' s.
Do you think a chrongraph is needed?

A chronograph is a nice tool to have, but it' s on my long list of tools I can live without. Besides, the club' s chronograph lives at my house.

I would like to have a good benchtop press because I really don' t fully trust those $35 pocket presses. So, I' ve got a good bit of pucker factor going on when I' m changing out strings and making adjustments to my string/cable lengths. The portables have those cables that get in the way also. The benchtop press is way better, all around. I' ll probably continue to live without one though, and go on dealing with tangled cables and the pucker factor. Really, I can do pretty much anything I need to do with a portable EXCEPT completely disassembling a bow. That' s one thing you really need a full blown press to do.

One tool that is very important to have and is very cheap to make is a drawlength measuring stick. Just get a full length arrow shaft, install a nock, measure out 20" or so from the bottom of the string groove and mark it every half inch out to the end. Or quarter inch if you' re highly industrious.