Lead Acid is sooooo 19th century, LiPo is where it’s at these days.
150W / 12V. Power = Current * Voltage, so Current = Power/Voltage = 15A. Yikes!
Now, depending on whether the motor is brushed or brushless (I’m guessing the former), you’d want something capable of taking at least that current, and that is suitable for the motor. Easy way to tell, how many wires coming out of the motor? Two = brushed, three = brushless.
I’d probably go for a 25A-35A, maybe something like this: http://www.sussex-model-centre.co.uk/shopexd.asp?id=27345
for brushed motor, or something like this: http://www.sussex-model-centre.co.uk/shopexd.asp?id=23892 for brushless
For battery I’d go 4S LiPo, something like this:
Kokam 4s 2400mah 30C
Type: 2400mAh 4S 14.8v
Continuous Discharge: 30C (72A)
Dimensions: H40 x W34 x L97mm
Weight: 260g
Balance plug: JST-EH
Charge rate: 2C
RRP £68.99 see our introductory Price below
SMC-RE-KC4S2400-30C
and then of course you’d need a suitable charger…