Came across your question moments after facilitating a security incident dry run for a SaaS with a 6 or 7 person core team (and a lot of sensitive data). Since many of the responses are focusing on the technical and reward/ransom aspect of this, I figured I could offer you some parallel thoughts on how to handle this from the business and liability standpoint.
There is quite a bit in this response, so please don't hesitate to ask if you want to talk this through directly. I can stand to offer 30min to provide some connections and make sure you feel equipped to go it with your current team. No cost of course and no nagging to get you on as a paying customer!
1. Insurance -
Assuming you have a policy geared toward technology companies, you may have coverage for "cyber" incidents. Look at your policy or call your broker to find out how to initiate coverage.
a) You probably need to tell them sooner rather than later that you are investigating an incident.
b) Ask for a referrals to the following specialities: tech/privacy law, forensics or security operations, and breach resolution vendors.
c) Find out whether the policy requires you to obtain a referral to use paneled providers (most do from my experience).
d) Find out any other requirements that might determine your ability for coverage down the line.
2. Legal (assuming American or similar legal system) -
Given what I know about your situation, I'd suggest that you retain a lawyer experience with security and breach response. This doesn't have to break the bank. The key point is to establish privilege and get help from someone who can navigate the statutory/liability landscape (it's a shit show). I can recommend one or two that are sensitive to the needs of small business clients.
3. Forensics -
If you have insurance coverage that will apply to this scenario, there is little reason not to contact a forensic or security specialist to validate your cleanup and ensure that the infrastructure is totally buttoned down going forward. Definitely follow the rest of this thread and digest the recommendations you're getting.
4. Customers/ Stakeholders -
Your customers and stakeholders will appreciate clear communication, whether during the investigation/response or after the matter. The lawyer I mentioned above will be able to help you think about communication with these parties as well as timing. If the incident turns into something more than it is right now, you'll be thankful for thinking this dimension through carefully.
5. Intruder -
Don't react carelessly. You don't know their motives or further plans. Is this a gray hat who is just wanting you to shore up your system. I'd be inclined to work with them and possibly even offer a reward. But I wouldn't go there without consulting legal counsel. Is this more about taunting or warming you up for a ransom request? Then get some folks with experience in your corner from the start. And be aware, your insurance might even cover a ransom request.
6. Law Enforcement -
Most of us prefer not to go here, but keep it as an option. Talk to your attorney about it.
7. Documentation -
Start keeping detailed notes. What are the steps you're taking to assess the situation? Who are you consulting? How are you measuring the risk? How are you preventing further damage? A breach coach can help you ask the right questions and record the information most needed to protect you and your customers.
8. Notification -
If you're in the US or EU, you very likely have breach notification requirements. Unless you are certain the intruder did not take or view any protected data (pretty much anything personal or payment related), I would treat the incident as a breach. In the US, you have 47 different state laws dictating notification requirements plus a few federal. Breach resolution services to the rescue if you have insurance. Breach coaches and lawyers may handle the little cases themselves.
9. Follow up -
a) Summarize the process in a short report and keep it in case you discover related damage down the line (or get sued).
b) Close the incident out with insurance and provide any documentation they need to process the claim.
c) Put a basic, written, practical plan together.
d) Build a relationship with a knowledgeable insurance broker (I can recommend a few).
e) Review, or update your insurance policy (or buy one).
f) If you can afford it, keep a tech attorney on retainer.
g) Set up a bug bounty through an established program (and if this intruder is well-intentioned, encourage them to use it in the future)