Mi mate - welcome to the forum.
The KG100 is a nice little grinder and will do well for plunger and drip filter and low end machines that use dual walled (perculating) baskets. The KG100 (a Solis, re-badged - made in Switzerland) will not however meet the needs of a proper ezpresso machine such as the Gaggia Classic. I have the KG at work and even after taking it apart and doing the tweak that gives it an even finer grind than standard factory (with resulting extra wear on the moving parts) it only JUST meets the EM6910 Sunbeams requirement - and even then I need to use very fresh beans, grind an instant before making the shot (as I always do anyway) and overdose and tamp very hard - and even then its not a great pour (that the machine can achieve with my Rocky) but a good pour and one that does me for work. At home I have the Rocky which serves it up nicely (and can choke if on a low setting) by commercial FAEMA 2 group. I reccomended to a mate recently the Rocky for her Gaggia Classic and do so to you...but you will be paying over double what you posted.
Some people on here are having success with the top of the line Sunbeam grinder. I have used it with the EM6910 at my brother in laws and with fresh beans we can achieve a nice pour and good grind (bit fluffy but it does the job). If you are serious about the dollars then check them out. From memory they can be purchased for about or under your budget.
PS - the build quality of the Rocky is far above the Sunbeam and the Rocky will satisfy you if you go for a higher end machine, although some members here have gone for a higher end grinder again for their higher end machines...