An easy solution is to download "Ethereum" and create a new wallet.
It creates a "seed" which are just some random words in a specific order. You need to remember (for example store in a password manager) this seed but never share it with anyone.
Now transfer the Bitcoin funds to this new wallet.
The backup is the "seed". As long as you have that you can access the coins from any computer at any time.

Like RGBKey says it's hard to comprehend this at first. Think of it like your coins are stored in the cloud. Everyone who has your exact seed words can access them. It's secure because guessing the seed is basically impossible.