Irishpilot talked about a higher rate of climb to cruise altitude at 250kts. Thats not accurate. Best rate of climb will be above 250kts in most airliners. If you want to save gas in a 737 you accelerate low (ie 1000ft) and you accelerate to best rate (about 280kts). You'll save about 10kg by accelerating NADP2 instead of NADP 1 and you'll save about 25kg by going straight to best rate. (Boeing info as best as I can recall).
SR 22 talked about cost index flying resulting in low climb speeds anyway..... Thats not accurate. Cost index zero will give you the least fuel burn, which is the best rate, which is well above 250 kits .
If you really want to be efficient you'll depart with the least flap possible and accelerate to best rate of climb as low as you can. There will obviously be slight adjustments for head and tail winds but that's the guts of it.