Flutter sleeves used to mean a dress that looked romantic from across the room and did something strange to your arms the moment you lifted them. That's shifted. The better versions now sit closer to the shoulder and stop well above the elbow, so you get the movement without the bit of fabric catching on door handles or trailing through your dinner. I think it's an improvement, though I still check the sleeve length before anything else.
The fit question is really about where the flutter sits and how much fabric is in it. Too much volume on the sleeve and you end up looking like you're being carried off by a small parachute, especially if the rest of the dress is already loose. Look for a sleeve that's gathered close at the shoulder seam rather than one that starts wide, because that's what gives you the shape without the bulk. The other thing to watch is the armhole itself, a dress cut too tight there will pull the sleeve flat against your arm and kill the whole point of it. Viscose and crepe both drape well and let the sleeve move properly, cotton poplin holds its shape but can look a bit stiff and sprigged if the sleeve is large, and anything with real stretch in the body (a jersey base, say) is forgiving if your size sits between two numbers, which it usually does with this cut.
If you've never owned one, start with a midi in a plain crepe or viscose, V neck or round, nothing printed and nothing with a tie waist fighting the sleeve for attention. That one dress will tell you whether you like the shape on you before you commit to anything more decorative. For colour, the easiest ones to live with are the in between shades, a dusty rose, a soft terracotta, a navy that reads as neutral rather than nautical. Black works but can look severe with a delicate sleeve, like pairing a good joke with a bad delivery. Pale colours show every crease from sitting down, which nobody warns you about.
These dresses earn their keep from late spring through early autumn, for anything where you want to look dressed without trying, a lunch, a wedding you're not in, a work event with a loose dress code. Start with the rose or the terracotta. Either will do more for you than you'd expect from one small sleeve.