Sounds like the driver was not using her turn signal, and you acted reasonably. Frankly, it does not matter much since this is a hit and run, and that the driver fled the scene tends to indicate an acknowledgement of fault. Put another way, the chances of a meaningful dispute of liability is practically zero.
You have no reason to wait for an investigation or the police to get a lawyer for a civil claim. The civil and criminal claims can run simultaneously, and since you were able to locate the driver, insist on pressing charges. That will take the discretion away from the police/prosecutors to some degree. If you know where the driver lives, you can likely run a public records search for a name, and then search social media to confirm the identity. Staking out the vehicle sounds reasonable, but be careful as hit and run drivers are often avoiding prosecution for other more serious issues. Do not confront the driver yourself unless police are present, because nothing good will come of it. You might take photos of the vehicle at some point if damage is shown. That helps in a civil suit later on. I am picturing a busted up, mid-90s Honda Civic, so the damage might be part of a rich tapestry of collisions.
As the lawyer mentioned, there is a possibility of an insurance settlement without a lawsuit. In fact, this is where most claims are resolved: usually an attorney negotiating with an insurance company. That said, a pre-litigation settlement will likely only happen if the at-fault driver is solvent and has liquid assets, or there is insurance at play. I am guessing this driver does not appear to have several thousand in cash at the ready. If the driver does not have insurance (another crime), and the car is unregistered/uninsured, the next best option is your own insurance. But if you have only basic, minimal coverage, that is probably not an option either.
Many states have what is usually called a “crime victims compensation fund” which comes into play in situations where someone is a victim of a crime, suffers financially, and the bad actor is unable or unavailable to pay. This is probably also an option for recovering something.
If none of that works, you can go after the driver personally for any assets she might have, and place liens on any real property owned. You mentioned apartment, so that might not work either. You can still get a judgment, garnish wages, and get money that way.
And if THAT doesn’t work, find something arguably unsafe about the intersection (stop sign obscured by branches, faded stop line, missing sign, bad sight lines, etc.), and sue the City/County for negligent design/maintenance. I know that sounds a bit out there, but you would be surprised how often that happens.
I hope that helps.