Now to get back to the topic…
As indicated previously, you should consider not paying off your mortgage faster if there is a potential need for emergency cash. I don’t know your living situation, but if you own your own home or are otherwise responsible for your heating situation, you will want to have enough on hand to handle any maintenance or replacement of your heat system. At least, if you live somewhere it gets cold. If you don’t, then maybe the same could be said for your cooling system.
If you do decide you need some of this money on hand, definitely take all that you need for months beyond the current one and put it into a money market mutual fund at a discount brokerage. Vanguard has the best rates out of the big three players in that space. Schwab is slightly lower but is a bit more risky, while Fidelity is significantly lower; Vanguard simply has a lower expense ratio on their money market funds. If you go with Vanguard (or Fidelity), you automatically have your excess cash invested in their money market funds. With Schwab, you have to manually buy and sell SWVXX, which isn’t a huge deal but is inconvenient. Because the income you earn on this fund is taxable and it’s unlikely that you can deduct your mortgage interest, despite the nominal return of these funds being higher than your mortgage rate, it’s probably not a +EV option to intentionally not pay off the mortgage instead of just having the money there to cover emergencies.
Once you’ve got that money market account set up, you can consider also buying short-term CDs that have slightly better rates than the money market, and at those brokerages, they offer the best rates that banks anywhere are paying. You just have to buy in even $1,000 increments. Fidelity does offer slices of CDs in $100 increments, but they’ll have a worse rate.
If you have no other investments though, assuming you don’t make too much money to be eligible, you should be maxing out an IRA of some sort with all that extra money you earn and don’t need right now. Whether a Roth or traditional is better depends on what your tax bracket that you anticipate being in during retirement will be compared to now. Most people in their peak earning years will have lower marginal tax rates in retirement, which makes traditional IRAs good. If you’re just starting out though, you might not be at that point yet. I hit that point last year, and will likely continue hitting that point if I get a similar-sized year-end bonus each year. You do have the option of recharacterizing your IRA contribution type until the due date of your tax return, which I took advantage of when I ended up making more money than I anticipated in 2022.
Note that if you expect your marginal tax rate to be the same in retirement as now, a Roth is better; they are not equal. In fact, the tax bracket difference needs to be substantial and not just 12% → 10% or similar, because with a Roth IRA contribution, you are also effectively getting to contribute the taxes that you would have paid on that money into the IRA compared to a contribution made to a traditional IRA where the money in the IRA is worth slightly less since you will be taxed on it when it’s withdrawn. If the difference is 22% → 12% as I anticipate for myself, the traditional is generally better, but for smaller jumps in tax rate the advantage of the Roth contributions being effectively greater can win out over a long enough period of time.