How intrusive is using VPN?
Solution 1:
They can only access your computer as much as any other computer on your home network can. If you have C:\ shared to everyone, they could potentially see everything on it - though this is unlikely unless you have a sketchy IT department. Otherwise, you should be fine.
That warning is up because all of your traffic is funneling through their network connection. This means that if you forget to terminate your VPN session and go surfing for porn or torrents, etc - it will all be logged on the company's servers.
Solution 2:
Connecting to VPN exposes you to "risk" from the side of your internal network. But there is much greater risk of being attacked from Internet. If you don't have evil enemies-hackers in your company and don't open up all the ports for all applications in the firewall then you should be safe :).