Hello,
I assume you want to make a true sine wave inverter. Such converters use a two-step approach.
An isolated transformer is required to step up the low voltage DC to about 180VDC. This DC to 180VDC converter can be a H-bridge type as well. You need more mosfets, but the transformer design is easier.
The second converter (that is fed from the 180VDC) makes the 110Vac via PWM (Pulse Width Modulation) of another H-bridge. This second inverter doesn't have a transformer, only filtering (with ferrite chokes and capacitors) to remove the switching products (20kHz...>1 MHz).
You need about 180…200VDC "bus" voltage as the peak value for 110VDC is about 155Vpk
Regarding the transformer, it is very unlikely that you can buy a transformer that fits your needs. So I think you have to design your transformer yourself. The design depends on: topology (flyback, forward, push pull, H-bridge), switching frequency, power requirements, etc.
As you are new to power electronics and magnetics design, you have to go a long way.
As you are working with potentially lethal voltages and power levels, safety must be taken into account also. What safety measures are applicable depends on the kind of application and the installation environment.