The six string Harley Benton progressive is a great bass for the money and very playable. Still got the deep lows that you'll need too for your style of music too, and the spacing isn't too roomy for your first 6.
I found that when I played a 5 string I just played it like a 4 with an extra string, just giving me 5 more low notes. I really struggled with a 5. Moving straight into a 6 string really makes you make the most of working across the fretboard. You can cover two complete octaves without a shift. I really had to stop playing 4's for a while though to really get comfortable on the 6. The muting was difficult at first, but soon comes naturally, as it does on your 4 with out even thinking about it.
The HB from Thomann will be an inexpensive way to find out. Trial and error the only way I guess, as every one is different.