Try not to get a VPN with a lot of RS players / tailored specifically towards the game. Jagex largely detects that type of IP address
To add on to what Nick said, Try to stay clear of any "Free" VPN. I made a fresh rs account on a free/shared VPN IP and was almost instantly locked out of my account before I even finished tutorial island. I did not even play it long enough to break any rules(Bot,RWT,etc). I fixed the locked status, but I decided to throw that account away in case it was flagged due to the VPN IP address.
I recommend searching for a VPN service that offers a Dedicated IP address addon. There is no way to know how many times they have recycled the Dedicated IP between customers, but you will have a greater chance of success than a fully populated Free IP server with tons of RS gold farmers. #IntsantFlagged
TL;DR - If you want to be extra safe with the VPN route, pay the extra $1.99 - $4.99/m for a Dedicated IP and make sure the site states that their Dedicated/Static IP addon is unshared!
Also, Do NOT login to the RS website/client/forums/game/etc with your main/legit accounts while the VPN connection is active. This applies in the opposite way too; Don't login to mules/bots on your home IP.
Separation is key to avoiding a chain ban on your legit accounts.
Hope this information helps!
Hey I'm just curious if any of you know how Jagex detects when you real world trade... And is it possible to do so without being banned?
They tend to keep their detection strategies to themselves for obvious reasons, but I personally think it is less of an automated thing and more of a personal research/watching thing(popular stakers are heavily monitored due to their publicly known massive wealth). It may also be loosely based on "Report Player" and possibly a script that searches for extremely uneven trades(Direct trading 2b for nothing,etc). There are tons of possibilities and nobody knows 100% how they detect it, besides themselves.
From what I've heard from other forum users, there is no actual "ban rate". It seems to be a random act of Satan.

Try to do what you think will best minimize your chances of a ban and stay safe.
Goodluck!