There are a ton of apps for this. I personally used one called Stock Trainer, mostly because that was the exact search I put into the App Store. The problem I found is that games like these are really only for mimicking day trading. If you buy and sit, you're gonna sit for a long time. Like years. I bet you don't want to wait years for a game to confirm your investment ideas. You should also be researching what options are available to you. Unless you can really pick stocks (which the game will tell you...in a year or two), your best bet for a buy and sit is probably an index. Minimal effort, and the best average return (generally said to be around 12% per year, but this is the stock market). There is also an online game that has you track individual stocks on a day by day basis using old charts. The goal is simple: best buy and hold. If anything, the game proves that for the average Joe, but and hold us the best strategy. I forget what the game is called, though it is linked from enough online resources you should come across it either in your normal research or through a quick search for 'stock game's or 'stock trainer'. I believe I found it through Investopedia. Best of luck, and do your research.
It's actually not that tough to build out a backtested portfolio in Google Sheets. The formula "=INDEX(GoogleFinance(C52, "PRICE", $B$60),2,2)" will give you the value of the stock symbol at C52 on date B60. Once you do that you can plug in any date you want (or do other stupid stuff) so that you know what it would have cost you to buy, say, Netflix on October 15, 2007. Once you have that, you can plug your numbers into a portfolio on Seeking Alpha or whatever and get instantaneous gains and losses not only for the day but for however long you've held your positions.
I found the online game. It selects random stocks, and you just try to beat buy and hold. Keep in mind you are at the far right, because you obviously can't see the future.