For lead acid your best bet is Adsorbed Glass Mat (starved electrolyte). The rating is at the C/20 current draw so a 40 amp hour battery is rated for 20 hours at 2 amp draw. The Peukert equation will determine how that decreases with additional current draw. So the poster above has 20 hours at 3.75 amps draw.
And for lead acid not going below 50% of capacity will give you a decent number of recharge cycles. From 300 to 500 if you use a very good charger. Deep discharges, even in a "deep cycle" battery will decrease the number of charges available.
So to size your battery, determine as best you can what your current draw might be using the motor as you intend. See if you can get a battery rated such that you are not exceeding the C/20 rating by much. The more draw the less total capacity. Lets say you decide to get that Wal Mart special and your motor draws 10 amps, most likely your real capacity will be more like 60 amp hours Still not bad as you would get six hours at that high draw if you don't care much about cycle life. If you want to keep the battery able to take more charge discharge cycles then the 10 amp draw would best be used for about three hours.
That is another advantage of the Lithium Ion battery. A better Peukert coefficient. Lead acid is about the worst for commercially available rechargable batteries. And the Lithium Ion can be discharged almost 100% and not lose cycle life which starts out higher than lead acid at about 1000 cycles.
Perhaps if you run some numbers you will discover as I did that Lithium Ion may have a higher initial cost but over the lives of the battery you will be much better off with Lithium than Lead Acid. And then there is the weight difference of four to one.
Hobie PA14 with a mod or twoSome random Modification Pictures