Tank Upgrade Cycling Help

I'm after some advice please.  I currently have an AquaOne 620 (90 ltr) with an external filter built into the lid. I've just purchased a 200 ltr tank and have following questions:

1) As I don't have room to run two tanks at the same time and therfore run through a fishless cycling process, I'm going to have to do a "with fish" cycling.  I have run my fish stock down and currently only have the following fish:
Brittlenose plec
1xHatchet Fish
2xCardinal Neons
1xBlack Widow Tetra
Will the fish be okay through the cycling process and is there anything I need to be sure to follow to keep the fish safe and healthy?

2) I'm looking at buying an Eheim external filter.  One filter is for 180-220 ltr tanks but I'm worried the filter would be working at its Max level so would I be better buying the next size up? Having never purchased an external filter any advice would be highly appreciated.

Thanks for the advice. The Aq u aOne was a spontaneous purchase many years ago which I've thoroughly enjoyed and the new tank is a 40th birthday present, and so can't wait for it to arrive. I think I've bored the wife already with all the reading up on new filters,  live plants and fish I'm looking forward to!