You can either buy Toriprime it's 10$ for 1 year, if you want a bigger avatar (animated images) and sigpic buy Vip, it's 7$ for 6 months (you need toriprime to have vip) or you can buy a bigger avatar and sigpic directly at the [Nabi] Profile and Item Customisation Store.
A Similar question was asked on avatar size in the Beginner Sanctuary Sub Forum, I have attached the appropriate response in the spoiler below
Increased Avatar Size
Your two options:
1. Purchase ToriPrime->Forum VIP subscription and accessing it that way. This requires two purchases as ToriPrime is required first before you can get Forum VIP. You can choose to just purchase a ToriPrime subscription for a 110x110px avatar if you so wish (All Perks or ToriPrime and Forum VIP can be found here: http://forum.toribash.com/showthread.php?t=465052
Originally Posted by Bart
Toriprime & VIP is a service available for purchase here.
Toriprime costs $10 for 1 year, and VIP costs $7 for 6 months, however you can only buy VIP when you have Toriprime.
2. Or alternatively you can visit the Official Nabi Profile customization store, where there is a subsection for 'Custom Avatars' where you can purchase a 150x150px avatar for $4 USD or a 150x200px avatar for $8 USD, this is permanent however it is worth noting that you do not recieve the other Forum VIP bonuses.
As you cannot purchase the privilege of a signature image from the Nabi Profile Customization Store, the only way of getting this is by purchasing ToriPrime 400x100px Signature image, and then if you want a larger image, you can purchase Forum VIP for a 650x150px Signature Image.
I'm afraid they are the only ways of purchasing said privileges as of the moment, feel free to post a thread in The Suggestions and Ideas Sub Forum if you think there should be alternative ways of acquiring these perks.