You won't need any special cables to connect to the TV, but you might want to invest in a SCART cable for your Amiga - you can get them on eBay for about £10 usually.
I'd call that a special cable. It's scart at one end and 23 pin d connector + 2 rca jacks at the other.
Otherwise connect it using the composite video (the yellow plug on the modulator - not the Amiga - and the yellow one on the telly). You can connect the sound up to the telly too but I prefer a proper HiFi. 
If you're going to connect via composite then worrying about the sound is probably the least of your worries.
If you want a real retro experience then you should use something like this:
http://cgi.ebay.co.uk/Hitachi-3D-Super-Woofer-Twin-Drive-TRK-3D80E-/150543223955 I think mine was a slightly later model, but these ones were everywhere at amiga exhibitions.
Many people like the Competition Pro joysticks, but if you get one make sure it's the original, not a USB one.
I was a huge competition pro fan back in the day. However I know they weren't everyones favourite and I'm not sure how well I'd cope these days. I remember the ball at the top made your hand sore after a while. You can get convertors to use modern pads on the amiga, these days I might be tempted to get one. However they will be expensive.
Your biggest task will be finding working disks. You can make disk images if you download "Abandonware", but the original disks are best - at least as long as they're still working.
There are not many games that can be legally downloaded from the net, however you're unlikely to get into any trouble from downloading a 20 year old game. You can get software for transferring images from a PC to a floppy on the amiga, but you need a crossover serial cable (I think you can bootstrap the software over the serial cable, but I never tried it). I used to transfer ADF's, but I had a high density amiga drive and used messydos or crossdos to read the PC disks on the Amiga.
There are also a couple of usb adapters that you can get now that do a similar job as the catweasel, which aren't all that expensive. One of them is read only at the moment though, I didn't look that closely at the other.
There are tons of Amiga games on ebay though.
