Your inverter need will be a function of the Watts used by your current appliance mix, multiplied by a fudge factor set by the total efficiency. You may want to oversize your inverter initially so that it can handle adding more appliances to your home, or so that you can utilize more capacity with your solar array as you add panels. This fudge factor is generally about a 15% surcharge; take the total wattage on your home, and multiply by 1.15 to get a good value for your load calculation worksheet.
Most inverters are 120 volts alternating current, but 240-volt alternating current inverters are available if you wish to run loads that require this. There are also step-up transformers available that attach to your 120-volt inverter that allow you to produce 240 volts alternating current, if necessary. In some cases you can also "stack" two similar 120-volt inverters together to provide 240 volts. Most inverters on the market also serve double duty as portable battery rechargers, which is a handy useful feature.
And, as with the advice on battery arrays, and solar panels, ALWAYS use the rated wiring. Don't get cheap here; this is a piece of gear that can cause house fires if the power cabling overheats.