Step one: is this a winch or a hoist? If it is a hoist, and you fail to use a worm drive to create failsafe load braking, you might kill someone. Never forget the ethics of your trade: setting aside the folks working in defense, don't design things that hurt people.
I'd encourage you to choose a AGM battery if you are looking for long life, or the new generation of lithium ion batteries for power tools if you need to keep volume and weight down. I'm out of date but, some years back, A123 was out front with this technology. Ignore the cycle life rating on lithium ion, it's going to last no more than 3 years from the date of manufacture, less if the product is rarely used: they like exercise.
The very low internal impedance of the AGM battery will allow much faster recharge, and, will suffer much less voltage depression under load, significantly increasing the performance of your winch.
If you are using a lead acid, size the battery to live between 50% and 80% charged. You'll be doing damage below 50% on a starting battery. A deep cycle will tolerate going down to 20%, but not as well as the manufacturer claims. If using AGM, size for 20% to 80%. Batteries have a life, and they lose capacity over that life. Beware the temptation to size the battery so it only achieves the duty cycle when brand new. Add in at least 20% reserve capacity for lead acid and AGM, more for lithium based technologies (like 40%).
The AGM will cost about three times as much as a good quality lead acid. Shale referred you to Lifeline. They are high quality.
Don't be tempted to switch power with standard relays, they aren't rated for inductive loads, despite the misleading horsepower ratings. Use a motor starter. These are very cheap and dependable:
http://www.mouser.com/ProductDetail/Magnecraft-Schneider-Electric/W199X-12/?qs=LQJGOuQCHKRYGVjEKfXYftw09xfiyRXjThey are available in different configurations and coil voltages.
If you are using any solid state drivers, include a protection diode.
The battery manufacturer will provide charging algorithms. Ignore them at your peril.
Learn the language of batteries: research and understand "C rate."
Disconnecting the charger when the motor is running is wise.
If you can squeeze it in, including a low voltage shutdown to prevent overdischarging the battery will significantly improve the dependability of the device. Including over current and over temperature protection to the motor will prevent rare, but smoky, catastrophes.
Or, if this is not a portable device, you can use a DC drive... Honestly, I think it is a better approach (In the interest of full disclosure, and to allow you the ability to judge the credibility of source, I'm ten years in manufacturing equipment and automation, ten years in battery and charging systems, first ten years as an electromechanical systems technician, working my way through school for a BSEE, second ten years started as a design engineer and worked my way to engineering manager--now I'm a corporate refugee, but that's another story).
N.B. I'd be advising you poorly to ignore the direction your mentor has given you. At the very least, give him control and your confidence. If you want to pursue an alternate direction than he has given you, involve him right away in the selection of direction you take. I've got a lot of reasons for encouraging you to consider this approach. I'm not going to tell you any of them. If you must know, then take this post to your mentor, and let him answer himself.
Good luck, and good for you for seeking multiple opinions. Now get started on some block diagrams.
Regards,
Mike O'