As far as things like Stash, etc., just remember that unlike having an investment firm managing your portfolio, you are going to have to do all the research on every stock you are interested in buying and assess the risk of said stock...AND make sure that things are set up so that the stock gets bought/sold at the price you want...AND monitor the performance of the stock on a regular basis to insure that the stock is doing what you want it to do and the company is still in good standing. Case in point, when I had my Roth IRA set up, the portfolio originally had Enron and Worldcom stock in it. Once day, I got a letter from my investment firm stating that they pulled Enron and Worldcom stock out of everyone's portfolio. Six months later, Enron collapsed...another 4 months later, Worldcom collapsed. Since the best way to protect your money from any volatility in the market is to have a diverse portfolio (your 403 is set up that way), that would mean spending a lot of time going over a lot of information in order to buy even a dozen stocks (and your 403 is more than likely diversified over a couple of hundred stocks).
But if that is something that doesn't bother you, and you have the time to do it...then have at it.