Please specify what model Amiga you have.
Regarding the Power Pack,
If your Amiga is an A500, A500 Plus, A600 or A1200, then the same power pack is used on all the models. Look out for an A500 power pack as they are the best ones.
Regarding TV connection,
If it is an A500/A500+ you will be needing the TV modulator which will allow you to connect to any TV with an RF input. If you buy an RF modulator, make sure it has the wire which connects the Amiga audio outputs to the modulator.
Another option is to buy an Amiga to Scart lead. They go very cheap, probably the same as a modulator and they give a much better picture on any SCART TV. A good Amiga-Scart lead will have the audio leads built in.
If it is an A600/A1200, the RF Modulator is built in. The Amiga-SCART option also applies on the A600/A1200 if you want a nicer picture than you would get using the RF Modulator.
Joysticks and mice are easily found on ebay and cheap too. A cheap good option for mouse would be the original Amiga "Tank" mouse.
With regards to the Amiga still working after being in the attic for so long,
If it is an A500 Plus, there is a chance that the battery on the motherboard is leaking. I would open the Amiga (500 Plus) up and remove the battery regardless if it has leaked or not. If it hasn't leaked yet , it will. If it has leaked, after removing it make sure you clean the board using a circuit board cleaner (spray) and an old tooth brush. Do not brush too hard or else you may damage the tracks. I usually remove the battery using plyers and wedging it side by side loosening it till it comes off. Again don't be rough or else you will damage the board.
A500 (NOT PLUS), A600 and A1200 do not have onboard batteries, but check for any memory expansions (especially A500) in the trapdoor underneath and check/remove the battery.
Another reason an A500/A500 Plus may not work after a long time in storage could be the socketed chips may have come loose and would need to be pressed in again. Unlikely but very easy fix.
A600s/A1200 are know to suffer leaky capacitors. Its unlikely but possible and if so it is repairable.
Hope that helps