I would suggest coding for Java 1.4.2 rather than 1.5 as it has a larger installed user base. If you are building applets, then you can't really use external libraries (without getting the user to install stuff manually), so you just have the standard libraries. However for a board game this is just fine.
I am assuming that the games will be stand-alone. i.e. not multiplayer. Multiplayer is tricky to do for a first project & also needs a machine to run a server for the game.
Roulette would be a fine choice to learn on. Here are some thoughts. You could draw the wheel using Paint Shop Pro, Photoshop or even windows Paint. The write some code to rotate it. This will be a bit tricky. Look at java.awt.Graphics2D class in the library perhaps. Some useful things are in there. When you press a key, the wheel can spin up and then gradually slow down and stop.
Once that's working, you could add the spinning ball. Making this move realistically could be tricky, but for starters, how about making it spin up and then spin down at a slightly slower rate than the wheel. Thus the ball moves for a bit longer than the wheel.
When that's looking good, you need to determine which slot the ball stopped in. Calculate the relative angle between the wheel final position & the ball final position. Scale and truncate the result to make an integer value representing the slot. Use this to index an array, which contains a list of the wheel slot numbers in the correct order. Print the number on the screen.
Then you can start implementing betting and scoring. You need a way to select a number (or red or black). Point and click with the mouse would be good. Maybe draw a representation of the board where the chips go. Maybe one click for each chip bet, although this would be tedious for large bets. Lot's of possible usability enhancements are possible here. You need to check the bets against the winning slot & amend the players chips after each play.
Lastly check when the player runs out of money. Game Over