Welcome! Glad you are starting to ask questions and figure things out early. It really helps.
You have gotten good advice so far, and this place is full of all kinds of good stuff. The other thing you will find is that there are lots of path that lead roughly in the same direction and to a sorta similar goal but are all different. It might seem frustrating if you want someone to just tell you want to do, but it is also good because there is no one right answer where all the other answers are wrong. There are just a bunch of good answers with different focuses and timelines. I didn't follow the optimum path, but I still got out early :).
Okay- make sure I got the questions.
Which retirement accounts should I prioritize? 401k to match then HSA. Then the others, it depends on your goals. Fast answer is see the investment order patchy listed, but your mileage may vary. See other posters answers and my answer below in story time. It can be as cut and dry as you want.
If I don't invest in a Vanguard account, will I not be able to take out withdrawals for early retirement?
I assume by vanguard account you are talking about a brokerage account where you just invest where you like. If so then:
Many FIRE folks use a 401k to Roth conversion ladder as a strategy. This allows them to take money out of a 401k and move it to an IRA then to a Roth (this is a taxable event) and then in 5 years take out of money as principle. So they only need 5 years of money to live on. This can only happen once once leaves a company where the 401k was connected.
There are other strategies as well like 72t (which i don't understand). But overall, you will not be locked in.
Which Vanguard allocation should I be focusing on buying? Is there a certain name that works best for people?
People here seem to like VSTAX Total Stock Market Index Fund. It is good general purpose. Some throw in some international or other flavors as well, but VSTAX gets the most love. That's what I rolled DHs IRA into for safe keeping.
Are there any accounts I should stop contributing to?
This will depend on your goals, and there will probably be disagreement here but I think overall based on your income and not knowing what your FIRE income will be, I would make the Roth your lowest priority. The power of the Roth is that you put in money that has already been taxed so that you don't pay taxes later (and you can take out principle). Well the taxes you will pay on the growth will be capital gains, which for married filing jointly is 0% up to $83,350 + the standard deduction (25,900)=$109,250. Then 15% after that up to $500,000+. So assuming the tax rates don't change a ton, you wont be reaping huge benefits on putting money there. Instead avoid the taxes now since they are a higher % and you need the cash. The principles in Roths make decent emergency funds since most people really think twice about taking the money out and using it.
How do I know where I stand with early retirement? Having trouble calculating net worth.
Okay so net worth. This is one of those things that has one of two purposes, 1-it can matter to you so you can compare yourself over time to see if you are meeting your goals or 2- you use it to compare to others to see how you stack up. There is no rule on how this is done. If you want to compare your pile to other people's piles to see who has the biggest pile then you need to scrape all the stuff together you can and see how big it is. I've seen people use investments, cash, house, cars, things, etc. If you just want to do a time point by time point comparison of self, then find the things that matter to you. I personally only use my investment piles, because those are the only things that matter to my FIRE date. To some people their pension matters, to some house (they plan to relocate). To some debt or negative costs (kids college) get factored in.
Now if you question was actually, how much $$ do I need to retire, that is more a math answer. We generally start with 4% as our quick and dirty answer. If you need $40,000 per year to live on then you need $1,000,000 invested. There was a study done (Trinity study) and follow ups and debates and stuff. There are lots of caveats to this (invested in what, do you really mean 4%, blah blah blah). But there are dozens of posts on lots of this. But the ball park to start you off is 4% or 25x your spending.
Story time - because why not :D. Above is the best practices kinda stuff. Below is more of what I did.
I (well we - DH and I) followed a very different investment path than most of the (very smart) folks here. Starting out I went for 401K match, HSA, then brokerage account. I wasn't a high earner so reducing taxes was less of a concern than growing money in an accessible way. I then used some of the growth of the brokerage account over the years to pay for a home down payment, student loans, DH's re-education, cars, etc. Eventually incomes grew enough that we started to max out my 401k, but that was only in the last few years.
Now we are living on our brokerage accounts for early retirement, starting at age 36 for me. So people can and do do it that way, it just isn't the optimum way to go about doing it. But I had to figure most of this out on my own before I found MMM and before 401k access.
Note- most people on MMM don't do it this way! They invest in 401k, HSA, Roth (which is a much more tax friendly strategy).