What pot size for 150 servings of sauce?

I would make up a small test batch and measure the amount of sauce you think is sufficient per person. It will vary significantly on the type of sauce, how "hearty" or rich it is, and whether you'll have a lot of side dishes or whether spaghetti is the only main dish.

Anyhow, once you decide on a typical portion, then just multiply the amount by 150 to see the total volume. For a typical example:

• If you assume 1/2 cup (4 ounces) per person (probably the absolute minimum you'd need), that would be 4*150 = 600 ounces. Since there's 32 ounces per quart, that comes to 18.75 quarts .
• If you assume 2/3 cup per person, that's 5.33 ounces*150 = 800 ounces/32 = 25 quarts. That might be a reasonable assumption for many sauces if there's just a single measured serving given to everyone.

If it's self-serve or "all-you-can-eat" or whatever, you might need a LOT more.

Always remember with a large pot that you'll need to allow space for headroom. If you want to cook 25 quarts of sauce, I'd use at least a 30-quart pot.

All of that said, unless you have experience cooking with large pots and have access to a stove with sufficient power and room (large pots are very wide and often quite tall), I'd recommend using multiple smaller pots. Sauce often needs frequent stirring, and that can be difficult with a very tall stockpot or something. Also, with a very large pot, it can often take a long time for the food to get to an appropriate hot temperature, so be sure your meat sauce is "safe" and heats fast enough.

(EDIT: I would clarify that the above is assuming an "American-style" spaghetti dinner. Traditional pasta in Italy served with red sauce usually has much less sauce, probably half of the above amounts. Again, I'd recommend making a test batch and measuring the amount you think is "correct" for your style of dish.)