Firstly, if you are going to get a chipper/chopper get a good quality one that can be maintained and serviced. (the cheap ones from Bunnings..like Walmart in US I think, they just die real fast). If you are good with engines you can self-service. It depends on what you are going to chip: think about max diameter you would like to deal with.. but my advice is to the the largest size thats practical for you. I got the biggest one I could move myself being a 5 foot two 50 year old female. It also is the biggest size that will fit in the back of my car....in order to take it to be serviced (which I've only done once in the 2+ years I've had it). Get a good quality engine...Down Under thats Honda or Briggs and Stratton.
You can chip/shred prunings and sticks,bark and leaves. Some things eg hibiscus look like they shred real well but are fibrous and tie my shredder in knots. Get to know your machine and whats in your garden.
Here's my strategy..not quite a closed system but as close as I can get at present:
Shreddable garden material gets shredded. The shreddings are either used as weed suppressing mulch (pref on top of newspaper which we get from our newspaper buying family members). OR they will compost quite fast, especially if you have a good balance of green and woody... ideally from small tree/shrub branches.
Compost goes back on garden and now the vege garden.
When I'm weeding I separate into :
-edible weeds ie edible by our voracious guinea pigs...saving money on GP food
- other weeds/ soft green stuff that won't shred goes into our green council recyling bin
- sticks kept for kindling for wood fire for heating in winter, or otherwise can be shredded if not too dirty. Large diameter prunings also kept for firewood or shredded.
- shreddible waste
Guinea Pig waste ( woodshavings + straw + uneaten food + POOP, lots of POOP) gets composted with or without shreddings. Compost goes back on garden.
Kitchen vege/fruit/ some other food scraps get put in Bokashi bin. Bokashi "tea" is drained off and used for fertiliser. The pickled Bokashi food waste needs to be buried and will rapidly break down to get great compost. I got sick of burying it, so now I "bury" it in a compost bin, covering with GP waste or leaves/bark.
This has saved me a fortune in removing garden waste, buying mulch and compost/fertiliser. Also reduced volume of garbage collection. You can substitute chooks for GPs or worm farms for Bokashi. Male members of family can provide liquid yellow fertiliser high in urea and nitrogen. ( mechanically trickier for girls).
Sorry long post, got carried away.