I started with an Omlet Eglu but soon moved on to a Green Frog Medium Chicken Lodge, as the eglu is really not big enough for more than two medium hens, although i did try to keep three in it and it was rather a squash for them. Having used both, I much prefer the Frog. For the same or less money, you get a coop which comfortably houses up to 6 hens, with two nestboxes instead of only one. It has proper perches, easily removeable - I found the sort of grid system that the chickens have to stand on in an Eglu was hard to keep clean and the chickens couldn't wrap their claws round it like they could on a proper perch. The eglu perch grid was hollow underneath, making it hard to get into the mouldings to scrub, whereas the Frog perches are just solid, rounded plastic bars, easy to scrub, and they don't really get dirty because the droppings fall out of the way rather than all over the perches, like they do in the Eglu. The Frog is up on legs, which is much easier on the back when you're cleaning it out, and also the hens can get underneath in the shade and dig around. In effect, it gives you a bit more floor space in the run. The build quality is excellent and the ventilation is far superior to the Eglu, with adjustable vents both sides, whereas the Eglu just has one or two holes in the sides, not sufficient in my opinion. Also on the Frog the door is adjustable - I never shut it on mine, but in the depths of winter I sometimes close it a bit, and you can get an automatic closer device for it if you wish. You can take the Frog to pieces much more easily - its basically a flat pack, whereas the Eglu is a moulded shape, not so good if you want to move it.
Quit e few of us on here have Green Frogs, and we are all very happy with the build quality and usefulness of these coops. I've never had redmite, and I think plastic coops are less prone to them and obviously easier to treat if you do get it. Plastic isn't magic, but is much easier to clean. If you already have redmite on your premises, you would need to be very careful about how you dispose of the old coop before installing the new, in case even one or two of the little beggars came across to the new coop and started it off.
There are some other excellent plastic coops on the market - many people like the Brinsea ones, also Solway's quite popular. I would suggest you try to see any you are interested in, and talk to people as you are doing on here, as there's nothing like hearing about other people's experiences before you buy. If you say whereabouts you live, one of our members might be able to show you their coop, I would certainly be very happy to do this.