We have bought several dildo's over the years and out of all the ones we've bought, only one doesn't taste nasty. Some have such a horrid taste them you can't get it off. Even worse, they burn when you use them.
What's the best material or company to use to avoid this?
Oh no, the toys you have are probably not body-safe if they're burning you! Like blueeyes said, avoid porous materials - rubber/'real feel' materials like Cyberskin etc/jelly/PVC - and stick to non-porous materials like plain silicone, which you can get in all different kinds of hardnesses and softnesses, and glass/steel/hard abs plastic etc.
Silicone toys like the ones Tantus, Vixen, and Fun Factory make (just as example companies, there a ton of excellent silicone toy companies) are incredibly high quality and can last you a lifetime as long as you take care of them and don't drop them into a wood chipper or something, so they're almost like investments. Also, silicone has never tasted weird to me but to be fair I'm not sticking it in my mouth that often!
I can tell you off the bat that that is not body safe.
It is made from TPE and Sil-A-Gel. Sil-A-Gel is a silcone jelly mix, which makes it porous (pores/tiny holes in the material), which means it will grow bacteria over it as you can't clean it properly.
TPE is a rubber, again non porous
FDA doesn't have any rules on sex toys, so basically a company can write whatever they want on the packaging and people will believe it.
Are the love honey jessica rabbits safe then? They say they are made from skin safe rubber?
I think they are regarded 'safe' as they don't contain phthalates. But they are probably still porous depending exactly what skin safe rubber blend they've used. Using a condom with them will give peace of mind, or of course just buying their silicone oh! Rabbit cousins.
This is a good read:http://www.lovehoney.co.uk/blog/2009/10/14/sex-toy-materials-phthalates-rubber-silicone/
I bought the Adrien Lastic Alive dildo recently, and I don't get any nasty tastes from it at all. The description says that it is silicone: http://www.lovehoney.co.uk/product.cfm?p=31237
I have chucked out my Doc Johnson and returned my other.
I really liked my 8inch but after a while It went a mucky gray color,(it was clear to start with) I kept it in a black toy bag. I think the dye must have seeped into the rubber. That put me off siligel, think I will be sticking with silicone! :)
For science, I just sucked my silicone dildo (http://www.lovehoney.co.uk/product.cfm?p=22767) and can tell you that it tastes of absolutely nothing 
The one you suggested should taste of nothing as it's made out of silicone too!