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Basically, you need #8879, #8884, #88002 and #88000. You can use #8878 instead of #88000, but you'd then also need #8887 as well. Both #8878 and #8887 are quite expensive, so for home use you're probably best just using #88000.
As for longevity, if you use good batteries, you'll probably get about 2.5 - 3 hours out of it, but this depends on a lot of things. You'll need 6x AAA batteries for the train, and 3x AAA batteries for the controller.
I know there are alternatives in which you can indeed control the speed (by controlling the voltage), but unsure which are best, I'll leave that to those more in the know.
I'd probably use an arduino instead of the IR receiver, just so I can add some other sensors, it could still accept IR commands from the remote, but also use distance sensors (stop if someone puts their hand in front) or sound sensors (eg. lights on / off if you clap). I've also go the charging boards so that shouldn't be an issue.
The only downside is that although I am sure I have an old 9V motor somewhere, I cannot find it! I'm not sure if I can modify a PF one to pick up charge via the wheels. I guess it might be possible using some old scalextric brushes that drag on the track instead of through the wheels.
There have been quite a few topics on Eurobricks and such discussing modding 9V motors etc, I still want to do it... 12V is also an option. There's a part that's basically a brick with the 12V track contacts on there and 2 contacts at the top.
Actually modding a PF one to do it is hard and requires custom wheels and such.. There used to be a bricklink store selling those but it's long gone and I've sent a message a year ago, with no reply...
Looking at what batteries are capable off and how much it costs, I do not think it offers me what I want, 3 hours is great if you look at it from a design and more playful perspective, but for me it will be a decoration piece, and if I have to keep switching/charging batteries I will end up not using it except for show, and with all the cool other winter sets out there, I would get more out of that.
The train track powered stuff does sound good. I saw that the straight pieces are 5 euro but the 'round' pieces are like 30 cents or something. So is it that the round pieces are just standard track and the straight pieces can do more? As planned now I would be looking at 4 straight pieces and 12 round to make a bigger circle, what are the options to make it go constantly? What would be needed and again how expensive would that be?
I used this link for info btw. I hope it's ok to post here: http://brickmodelrailroader.com/index.php/2017/02/07/battery-powered-vs-track-powered/
Maybe those parts are cheaper than 9V track -- but 12V motors, transformer etc may turn out to be more expensive...