I don’t have a problem getting in and out of a meadowbrook, but they aren’t really ideal for trail driving, too many ways to catch stuff on them with the fenders sticking out. If you do end up with a meadowbrook you can unbolt the fenders and make it less bulky looking and easier to maneuver.
Wooden wheels are fine on trails - think about what the roads were like when wooden wheels were used. Muddy, rutted and uneven. Just make sure they are solid and tight. Also, larger diameter wheels make for a smoother ride as they just roll over smaller bumps and ruts, and the carriage is easier to pull.
Another thing to look for is the height of the seat. You want to sit high enough to see over the horse, but not so high you feel unstable. Here is a chart from the American Driving Society (ADS) to give you an idea of the measurements to look for. The main measurements you need to check fit are shaft tip to swingletree and height of the shafts when they are level. Wheel size is shown in the chart, but that will vary widely depending on the type or design of the cart. A road cart or meadowbrook will have larger wheels while something like a Frey Sprint cart uses a smaller diameter for the same size cart.
http://americandrivingsociety.org/Members/NewDrivers/DrivingVehicles.aspx
Also, if you have never actually driven before, please find someone in your area that can help out and check adjustments. Another point is with the Standardbred, were they trained for carriage driving after racing or were they only trained for racing? If they haven’t been driven outside racing they might need time and training to adjust to the breeching and heavier cart.