I have about $200,000 cash to leave my only child, should I have a Will or a trust?

There's a lot more that should go into a decision like this than the cost of probate.  For example, you need to consider the possibility that you might need nursing home care later in your life, and if you want Medicaid to pay for that, you'll need to show an extremely low net worth (this might be something like $5,000, perhaps less, 5-10 years from now), and you can't give away your money at the last minute to qualify, because there's a 3-year "look back" period where anything given away or sold for less than fair market value is added back in.  Talk to an attorney familiar with "Elder Law" for details, and ways that you can legally plan to deal with this if necessary.