Your like me! I love good wood on a stock. I would say for the money look at the Weatherby Vanguard Deluxe. My brother has a 257 Weatherby Vanguard Deluxe and it has fantastic wood on it. Winchester Model 70 super grade also has really good wood. Which ever you pick if your at a store and they have a few in stock, ask them to bring all of them out and you hand pick the best they have. If shopping online ask them to send pictures of what they have in stock and hand pick what you like.
As far as 270 vs 30-06 they are both fantastic cartridges! The '06 may kick a little harder than the 270. But the '06 has a better range of bullet weights available. You can take any wildlife in the lower 48 with either one. Pick the one you like. Even better may be to find a friend or someone who will let you shoot their '06 or 270. And go from there. As for the Remington 700 I own one of those as well in 25-06 and it's a fantastic shooter! Never had any issues with it at all. Most of the time you wont find beautiful wood on a Rem unless your lucky (I was mine is tiger stripped from the back of the stock right through the forend)
Good luck shopping.