I am working on the same thing. I'm still in the model building phase and I still need to complete my backtesting framework. You seem to be ahead but I've already looked into the trading API process.
Go with whatever broker offers a trading API obviously, and has a fee structure that matches your trading strategy. If you can afford to lose a bit on the trade through commissions and your strategy is swing trading then you can pick pretty much any broker. If you need specific fill times and commission percentages before your strategy pays off then you are stuck with Interactive Brokers ($10k minimum[1], low comms, fast exec) or Robinhood (low minimum, free comms, slow exec). And technically Robinhood doesn't have a public API[2] so you would have to do a little reversing of their app's messaging. And then there's terms of service... yeah. Probably not a big deal for a small fry like yourself.
Next would be testing. You've got isolated tests with historic data but try get a broker that has a paper money version. TDAmeritrade's paper & api is good (but they are expensive). To be clear you would be using your algo to trade in a paper money account. That lets you get more realistic trade tests and if you blow something up you are still ok!
Keep in mind Robinhood is free because they are paid to route your orders to hedge funds and they are re-ordered in the book. You will get ok price execution through them but never the best. One thing you should include in your backtests/simulations is order execution delay and fill price variance. If you place market orders they won't always fill at the quote price. If you place limit orders they may take a while to fill (or not at all) unless the price is within the other side's order prices.
Last is the pattern day trading rule. Make sure you have a strategy that won't make more than 3 day trades in a 5 day window, otherwise your account might get suspended for a few months. It's a pile of horses but you can get around that by simply having more money in your account. > $25k will buy you unlimited day trading privileges.
Just curious what your strategy is based on if you don't mind giving a few details.