Unless you are rich you should forget about AmigaOS4.0 cos a Cyberstorm PPC (the only PPC card for an A4000) will set you back more money than a top spec modern PC.
Get AmigaOS3.x and enjoy it.
I'd remove the battery as soon as you can. I wouldn't bother replacing it. I've not.
Networking on Amiga 4000 is expensive. You'll need to pay at least €75 for an X-Surf ethernet card.
A better buy if you MUST have networking would be a €120 Deneb USB2.0 host card + a €5 USB Ethernet dongle. You get to use all the USB devices you like and Deneb's Flash ROM means don't need to buy Kickstart 3.1 ROM chips to use Amiga OS3.9.
I say for the moment, keep your money in your pocket. No need for a network to transfer files. Buy a
€5 IDE->CF panel adapter & Compact Flash card. It fits easily in an expansion slot in the back and allows you to use a Compact Flash card as the primary hard drive. You can take it out and install the OS / transfer files on your main computer quickly and easily.