Any compressor that needs a magnetic starter will come with it as part of the compressor, unless you are buying used where they sometimes sell them without. The size recommends depends on how long you plan to use the die grinder. If you plan to use it for minutes straight, you need enough CFM to keep up with it. Typical 0.33 HP rotary air tools use 17-19 CFM, 0.50 HP use 23-28, and 1HP use 35-43 CFM. Some people think this advise is crazy and have said nobody uses a die grinder 24 hours a day. No, they don't. But if you need it for 10-20 minutes, then you need enough air otherwise you wait on the compressor. If you only need it for 30 seconds, then a smaller compressor with a larger tank will suffice. The least expensive IR dual stage is about 15.8 CFM which is marginal for prolonged use of a die grinder at full load. The impact wrench is used in bursts, so even though it may be rated for 37 CFM you don't hold it continuously for long enough to matter. It probably work fine with your current compressor. The air ratchets typically use more air because they run for longer periods. This may be marginal with your current compressor. Air hammers typically use the least, only about 10-12 CFM and is probably fine with your current compressor unless you are running the air hammer for a long time.
Two stage is not strictly necessary, but the higher pressure sure is nice. Typically air tools run at 90 psi. This is often the 'cut-in' for a single stage compressor. But the regulator and hose usually take 10-15 psi off that, so you're at 75 psi at the tool before the compressor kicks on. You can fix that by adjusting the regulator, or replacing it with an adjustable one. Dual stages typically cut in around 145 and shut off at 175. This gives you about 40% more air reserve, and will avoid low pressure situations unless you are using an air tool that uses more than your compressor makes and you run it down that far. There isn't much special about IR compressors. I would get a 5HP 17-19 CFM dual stage compressor with a 60-80 gallon tank if I was in your situation. That's probably not the cheapest IR dual stage, but one level up.