I don't think there is any real advantage of a gas syringe compared to collection over water.
H2 is barely soluble in water, so that won't cause a problem.
The tolerance of measuring cylinders is comparable to (and sometimes better than) gas syringes, so precision isn't the issue.
Measuring cylinders (in schools) are available in a larger range of sizes, which is rather handy.
Both are easy to set up, use and read. Admittedly, gas syringes are quicker, but this shouldn't be fatal.
If you plan to do something like measuring out different masses of Mg to see how volume of H2 is produced and then do the mole calc to see how things went, it is worth doing the maths...
What mass of Mg will produce 100 cm3 of H2 (the standard size of gas syringe). You'd no doubt want a range of masses of Mg, to show a directly proportional relationship. So you'd want to produce something like 30-90 cm3 of H2. What mass of Mg would be needed to make 30 cm3? Do you have a balance able to measure than mass of Mg accurately? Or should you be scaling the whole thing up? Do you have the gas syringes available for this volume of H2? (I'll bet you have the measuring cylinders). BTW, I haven't done the maths, I'm using my (rather large) gut.