Technically, you must choose a cartridge that will:
a) not be obviously incompatible with your tonearm, and
b) not be obviously incompatible with your phono stage gain, and
c) not be obviously incompatible with your phono stage input impedance.
According to the information posted at http://www.cartridgedb.com/
your Sumiko Premier FT-3 has an effective mass of 14gm. That makes it generally compatible with a wide array of medium compliance cartridges. Anything with a dynamic compliance around 11-15 CU is unlikely to have any obvious problems (which is all those formulae are good for).
Your phono stage gain, as the KAB site and Syntax said, should be fine for any cartridge having an output of 0.5mv or above, which means the majority of MC's. Except for the ubiquitous Denon 103 (which might not be a great match for your arm) most really LOMC's cost more than your budget.
What input impedance setting(s) is/are available on your phono stage's MC input? This will determine the coil impedance(s) that will provide optimal frequency response in your system.
So, we know you need a medium compliance, mid-output MC with an internal impedance of ____ ohms. There are (probably) hundreds of cartridges meeting these criteria. How to narrow the field to brands and models?
Well, we can't. Without knowing something of your musical and sonic preferences and priorities, recommendations would be meaningless. If you posted this question on some forums you'd receive a slew of answers that all boil down to "I like X, I like Y, I like Z."
Most posters on this forum know better than to offer meaningless answers that can only confuse or mislead. Should I tell you which medium compliance, mid-output MC's I like? Should Syntax? Should Raul or Elinor? None of that would mean anything, because none of us knows what YOU like.
Help us out a bit. Answer the impedance question and talk about who you are, musically and sonically.