Can I assume because you say 'till the garden' you are talking about a veggie garden. I use very fine woodchips in my veggie garden that have first spent some time in my neighbors stables. If you till them into the garden they may rob your soil of nitrogen, although if you have clay they would help the lighten the soil and you can add extra nitrogen after you plant. I don't till my sandy soil at all, but keep adding rough material to the surface. After almost 20 years at this site my soil is a basic black, or close to it. If I had big enough cages my tomatoes would grow 10 feet tall. So if you don't till the wood chips in, pull them aside and then clean your garden. Soil needs protection from winter weather, so if you don't plant a cover crop a good mulch is the next best thing. If it is thick enough, it will deter cold season weeds like chickweed from getting a foothold. In general almost any mulch is better than no mulch, and it is understandable if it takes awhile to learn how to handle a particular type.

You also might want to try permeable row cover for plants like tomatoes and melons - it stops the weeds but lets water through.

For flower gardens, you just leave the mulch on top, and let it feed the worms/micro herd, adding to it each year as needed. For veggies, you can leave the mulch be. If you are fall tilling, then I would till it in, assuming that by next spring it would be mostly decomposed. Any nitrogen loss is only temporary, until the wood chips are fully decomposed. You might want to add a little extra nitrogen when you plant, to avoid any temporary nitrogen loss do to the wood chips. IMO, the best mulch for veggie gardens is grass/straw/leaves, with a thick layer of paper under them. I haven't used woodchips, as I don't have a free source. The mulches stop the weeds, conserve water, usually free, and enrich the soil. For a new garden, I usually only have to till the first year or two, since the mulch keeps the soil very workable. I also put 2-3 feet of leaves on the garden in the winter for all the reasons above, moving them when I plant. This year I planted onions with no mulch between them, and after several weeks of no rain the soil was very dry. But when I uncovered the section I wanted to plant beans in, the soil was still damp. Mulch is wonderful.

I'm alot like Annie, thick layers of newspaper with straw over the top in my veggie bed in the summer. In the winter- as many leaves as I can get. I no longer till as well, just put holes where I want to plant. In the fall I rake up the straw and put in the compost, in the spring the same with the leaves.