Mr. Nuttall as you probably know, an "organ" has at least three divisions: lead or melody (traditionally the upper manual), harmony (lower manual), and bass (pedal division.)
If you're NOT going to add MIDI pedals to your keyboard, an arranger is your best and only hope of emulating an organ, because it would be amazingly difficult to play both harmony and bass with your left hand on any other type of single-manual synth.
One of the defining functions of an arranger is "auto bass chord" (it's called by different names by different brands.) Put simply, the bass follows the chord, or in better models, the lowest note played in the chord section. This partial automation allows even a relatively unskilled player to play the bass and chord at the same time, yielding a passable result. And it isn't by accident. Arrangers evolved from "home organs," which themselves evolved from electromechanical organs like the B3. So in a certain sense they are a widely available and comparatively affordable evolutionary descendant of the organ.
Regarding styles, you really should listen to some of Yamaha's "free play" styles, which are not modeled on specific pop songs, and are very useful for liturgical music. Although Yamaha was the first to commercialize the concept, similar styles can be programmed for any of the major brands; I have done so and have shared my experience previously on other forums. Casio's "String Quartet" style is similar to a free play style, that's why I mentioned it. Finally, most arrangers have limited auto bass chord functionality even when not using a style. These could be re-voiced with organ tones, or plumbed through MIDI to an external tone bank like Hauptwerk.
I also mentioned that low-end Yamahas such as the PSR-E373 DON'T recognize chords with altered bass, so there are some organ scores that won't ever sound right on them. They also don't accept free play styles, that style structure is reserved for better models. So although cheap to buy, Yamaha's entry-level models are a dead-end. If the original poster (David) is serious about this, he's better off with the Casio, or stepping up to one of the mid-range instruments that Biggles listed in his post.
