I believe Risa are one of the top standards in commercially available electric ukuleles.
They appear to specialise in that field, and have both nylon string and steel string electrics.
Here are my two beloved Risa steel string ukes
Risa Uke-Electric Tenor. DGBE tuning (Baritone uke). Lipstick single coil pickups
Risa Les Paul style Tenor. GCEA tuning (low G). Humbucker pickups
For being electric, I've grown a preference for steel-string electric ukes.
I've owned Eleukes and Risa nylon string electrics in the past. They're great fun, but don't feel truly "electric" when compared to an electric guitar.
They're still partly 'acoustic' in my opinion, due to the nylon strings and piezo pickups designed to reproduce acoustic sound, rather than electric sound.
If you're after something that behaves more like an electric guitar version of a ukulele, I suggest saving up for a steel-string electric for the real deal.
But unfortunately, Risa steel string ukes are quite pricey. In my opinion, it is worth it for the quality, but it would be nice if there were less expensive steel string ukes available.
I hear Eleuke are working on some. I imagine they may be closer to your price range. The Risa's are about double your current price range, unless you find a second hand deal.
ps: Just remembered.
Konablaster steel string electrics from Elderly Instruments may be more affordable for you.
Though I've heard there are some issues of strings sounding unbalanced due to the magnetic poles not lining up with the strings.