What units should use for velocity prediction equations?
In principle it does not matter which system of units you choose to use as long as you are consistent. It is however always easier to do everything in SI units and then convert the result of your calculation into whatever unit system you prefer. Using inconsistent units has resulted in many accidents including the crash of the Mars Climate Orbiter. That is why NASA is using SI units now:

Public Law 94-168, §2 requires use of the International System of Units for measurement in U.S. Government programs, &quot;except where impractical.&quot; That requirement is reflected in NASA policy, NPD 7120.4. That measurement system, formally known as the &quot;SI&quot; system,&quot; after its name in French, Systeme Internationale, is almost universally used by all countries except the United States. Use of SI measurement is growing in importance for international trade.

In your case, the mistake is using Watts for power, which is inconsistent with the remaining units you chose:
$$ 1 \, \text{W} = 1 \, \text{kg} \, \text{m}^2 \, \text{s}^{-3} \neq 1 \, \text{lbm} \; \text{ft}^2 \, \text{s}^{-3} $$
If you want to use imperial units, you need to convert your power to $ \text{lbm} \; \text{ft}^2 \, \text{s}^{-3} $, which can also be expressed in units $ \text{lbf} \; \text{ft} \, \text{s}^{-1} $ where lbf is the pound-force (lbm is the pound-mass)1. Horsepower is different again and I would advise against using it because there are many different definitions, the most common one being that 1 horsepower is equal to $ 550 \, \text{lbf} \; \text{ft} \, \text{s}^{-1} $.
If you stick to SI units (kilogram, meter and second), you can use Watts for power and you will get your velocity in meters per second, which is easy to convert to any unit for speed you want.

1 $ 1 \, \text{lbf} \approx 32 \, \text{lbm} \; \text{ft} \, \text{s}^{-1} $ (Thanks to Michael Seifert for the clarification), see also this question on engineering.SE.