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.
Best Answer
You can use the same board (I often do), but you must wash it in hot, soapy water in-between. Usually there is plenty of time to do this while the meat is cooking. Because bacteria grows exponentially, I'd recommend washing the board soon, even if you aren't going to reuse it, to prevent accidental cross-contamination.
If you're using one meat board, you should also wash it between different kinds of meat. For example, pork and chicken typically have different bacteria risks and different cooking temperatures because of those bacteria. If you cross contaminate, then safely cooked pork may still have a risk of salmonella.
And, of course, you should wash your knives, spatulas, tongs, etc between handling uncooked and cooked meats.