Your primary defenses against cross-contamination include proper planning in the order of what you're cutting and proper cleaning between uses. In the case of your stew, simply cut the vegetables first and then cut your meat. Doing so in this order you won't need to wash the board between the vegetables and meat. If you want to expedite the cooking process, then either use a separate board for the meat first so that you can start browning it while cutting the vegetables, or simply wash and re-use the board. A good scrubbing with hot soapy water is fine for your knife and board (including wood boards).
As mentioned previously, if you're still concerned about bacteria you can rub the board with lemon juice or vinegar which will kill any residual bacteria.
Using separate boards that are relegated to specific meat vs. vegetable duty isn't necessary as long as you're properly cleaning your boards. A board only used for meat items is just as liable to transfer bacteria to the next item being cut on it if it isn't properly washed between uses. That being said, if you're properly cleaning them then it's fine to cut vegetables on a board that's also been used previously for meat.
As for cutting boards, your best bet for the care and maintenance for your knives are either wood or composite materials (usually a laminated product of paper and resin - "Epicurean" being a prominent brand.
Never use a tempered glass cutting board or other hard surface (granite, marble, Corian, etc.) as these are heavily damaging to the edge of your blade and unsafe for you as there is nothing for the knife to bite and grip into and it's much more likely to slip and cut you.
Plastic cutting boards and mats aren't very good on your knives and the boards in particular are either too hard and dull your blade prematurely or are soft and end up with lots of cuts and grooves which then trap food. People often have a false sense of security with plastic boards believing them to be "non-porous". As the board is used, food material ends up crammed into the cuts and grooves and while the boards can go into the dishwasher, that only removes the surface grime, not that which is impacted and over time you increase the potential for bacterial growth to occur.
Wood boards (including bamboo) are much better on your knives but to maintain them in good condition you need to properly maintain them. Periodically, when they look dry (kind of like chapped skin) you need to oil them with mineral oil. The mineral oil you buy at your local drugstore or grocery store pharmacy is fine, no need to buy fancy "block oil" in gourmet shops. Don't use vegetable based oils as they will go rancid and transfer the flavor to your food. I like to give the cutting board a heavy coating at night, let it soak in overnight, and then buff off anything that didn't soak in. This will keep your wood fibers soft and supple so that the board won't split and crack, the fibers will swell back together making it more "self-healing" as you cut on it, and the oil in the wood will repel liquids that would otherwise try to soak in. When a wooden board gets marred and nicked up you just need to take it to the garage and give it a good sanding before dusting off, rinsing and re-oiling.
Don't use bleach on boards (plastic or otherwise) as it will typically leave a distinct smell in the board.
I think what you want to do is this, cribbed from this book, which has an excellent step by step guide with pictures:
Remove the wings. Stand the chicken on its neck, legs point to the ceiling and breasts pointing away from you. slide the cleaver between the body and wing, cutting through the joint close to the body. You should slide the knife between the joint cutting only the tendons, not the bone.
Remove the legs. lie the chicken on its back one leg near you, one leg away from you. slide the knife between the joint near the body, again cutting only tendon not bone and remove the leg.
Separate the thigh from the drumstick, again go for the joint. If you want the legs to be in smaller pieces then you can cut each thigh and drumstick in two with a firm action. You have 2 choices for technique
Start with the cleaver tip furthest from you on the board, place the thigh under the blade and push down firmly and quickly. you should cut through the bone.
Chop through the bone by lifting the cleaver in the air and bringing down hard and fast. This has better chance of a cleaner cut through the bone, but you need to be a better aim.
Split the carcass in half. Stand in the same position as 1. and with the blade parallel to to your body cut down through the carcass so you have the back and the breast in separate pieces
Remove the breast from the bone by sliding the knife (might want to use a smaller knife here) between the meat and the bone.
Remove the backbone out of the back, kitchen scissors are easiest. you can skip this if the back doesn't have much meat.
Cut the back pieces into nice size pieces across the length.
Slice the breast pieces crosswise into nice size pieces
Reassemble the chicken on the plate with the breast meat on top of the back pieces
this picture doesn't really do it justice, but until I can find a better one...
this video shows it being done with a bit more force and not for presentation, but might be more what you are after
Best Answer
A chinese style chef's knife, also known as the cai dow, or vegetable cleaver(trial subscription required, but an excellent article), is superficially similar to a western cleaver. The cleaver is typically a very robust blade, thick and weighty, meant for separating meat at the joint, splitting ribs and chops, and other tasks that require a lot of weight and a stiff blade.
The chinese chef's knife will be much thinner and lighter, comparable to a western chef's knife or Japanese nakiri. The broad face is for scooping up ingredients from the cutting board and controllability rather than mass and strength. From a brief blog entry from Kitchn on the knife -