Looking for batteries to power a project I'm working on
80 Watts. 100 Watts to be conservative. That times 16 hours is 1.6 kW*Hrs.

In no particular order here are some of your options:  


Lithium ion: if you don't care if the batteries degrade within 3-5 years, lithium ion batteries would work. They'll be light and small.
Lead acid would also have degradation issues in the 3-5 years range. They're heavy but cheap.
Nickel-iron batteries have a very long life time and by weight have more energy than lead-acid. By volume they have less.
Lithium iron phosphate have long life times and and have about 1/2 the energy density of lithium ion and about as pricey.
Nickel Metal Hydride (NiMH): Next most energy dense technology behind lithium batteries. Cheaper than lithium type batteries. Limited lifetime to 3-5 years varying largely depending upon use/abuse.
Nickel Cadmium (NiCd): requires a smart charger to prevent memory effects. Older technology, less energy dense than NiMH, cheaper than lithium ion.


Your choice really depends on what you're after. How portable does it need to be? How much of a factor is cost? Which should be weighted more, energy density or specific energy? How important is lifetime of battery to you? 

All of these battery types have relatively high usage in some field, so they all have some advantage or allow for some balance between options.

If it was me, for a battery that size, I'd likely go towards something pre-manufactured to be near my specs. If you're interested and knowledgeable in battery balancing, charging and discharging, you could work with individual cells to come up with a nice solution and possibly save a bit of money. Otherwise, you're best off buying something off the shelf with your specs: 20V, 1.6kWHr.