Sorry, can't recommend an inverter. Others have recommended a Kill-o-watt (r) meter to see what you really need.
BUT: I can say these things:
induction motors will be happier on a sine inverter. and they want a BUNCH of surge capacity to get up to running speed. (figure 5 seconds? That's beyond the limit of any inverter I've ever seen. Remember the inverter isn't going to pull up a motor as fast as a genset or the grid.)
Universal (brush) motors (Circular saws, drills, routers, dremel tools, etc.) don't care what sort of inverter you're using; they'll even run on 120Vdc just fine. the variable speeds will be touchy but otherwise fine on anything that crosses zero regularly; if you use them on DC, the variable speed won't work, but the motor will happily run at 100% RPM.
1200 watts out of the inverter is 100 amps at 12 volts, with no loss. That's a bit much for a single deep-cycle battery. By the time you figure copper loss, conversion loss, etc, at 1800 watts you're going to be pulling close to 200 amps. you're in starter-battery or electric vehicle territory at that point; most import cars need about 200 amps for 2 seconds or so to get started.
Also, that 115 Ah rating is assuming you take 20 hours to drain EVERY last joule out of the thing. for durability, figure on drawing no more that 1/2 that in 24 hours. . . the EV guys figure no more than about 20% of your capacity per hour for the sustained (more than 30 sec) discharge rate. True, you can get more, faster, but you're going to pay for it in physical battery deterioration.
better get SEVERAL more batteries. . .
Run the big stuff on the genset. Drills and the like will be happy on an inverter.
Get a big bottle of CO2 for your air tools, if you have any. A 20lb bottle and 150psi preset regulator ran me about $200; fills are about $2/a pound. (a 20 lb bottle lasts me a LONG time. . . I use it for airbrushing and tire filling, and get about 6 months of occasional use per fill.) Your tools will last longer, too. . . no water = no rust. just remember to oil them! I figure a pound of CO2 will give the same service as 1/2 gallon of gasoline in a construction compressor, assuming mostly idle time.