Sorry Mark but this is going to be a long post.
The first thing you need to do is determine the total load that the inverter will need to supply. You have mentioned that you have a fridge & a freezer. The inverter must be sized to accommodate the starting current for each of these devices, plus the extra load of the T.V. & phone/fax etc. You may need to look on the compressor of both the fridge & freezer to get the info you need. If possible, try to find the L.R.A. (locked rotor current) of each compressor. This info may be in any operation manuals (if you still have them). If the L.R.A. is not indicated, use the F.L.A. (full load current) & multiply it by 4.
Don't forget to include any lighting.
Inverters typically have 2 ratings (like a generator)...a "continuous" rating & a "surge" rating. You may also notice that generators & inverters are sized in VA (Volt Amps) & usually not kilowatts...there is a good reason for this. Let's do a sample calculation;
Formulas - W (power) = E (volts) x I (current) x P.F. (Power Factor). We need to find the current (I) so;
I = W divided by (E x P.F.)
Power Factor is used if you can't find the FLA or LRA of the fridge/freezer & only the wattage is known. Note - I have assumed that the fridge & the freezer have a P.F. of 0.8.
Continuous Load calculation.
4 x 60 Watt incandescent lights - - - - - - - - - - 60 divided by 240 = 0.25 Amps.
1 x 300 Watt fridge - - - - - - - - - - - - - - - - - - - 300 divided by (240 x 0.8) = 1.5 Amps.
1 x 300 Watt freezer - - - - - - - - - - - - - - - - - - 300 divided by (240 x 0.8) = 1.5 Amps.
1 x 300 Watt TV - - - - - - - - - - - - - - - - - - - - - 300 divided by 240 = 1.25 Amps.
1 x 100W "printer" fax/phone - - - - - - - - - - - - 100 divided by 240 = 0.4 Amps.
Total continuous Watts as listed - 1060 Watts.
Total continuous current as calculated - approx 5 Amps.
Surge Load calculation.
The only items that will have a surge current are the fridge, freezer & TV.
1 x 300 Watt fridge - - - - - - - - - 1.5 Amps x 4 = 6 Amps.
Fridge surge - - - - - - - - - - - - - - 6 Amps - 1.5 Amps = 4.5 Amps.
1 x 300 Watt freezer - - - - - - - - 1.5 Amps x 4 = 6 Amps.
Freezer surge - - - - - - - - - - - - - 6 Amps - 1.5 Amps = 4.5 Amps.
1 x 300 Watt TV - - - - - - - - - - - TV surge is approx 0.5 Amps.
Total surge current - 9.5 Amps.
Your inverter will need to supply a continuous current of 5 Amps.
Your inverter will need to supply a total surge current of 5 Amps + 9.5 Amps = 15 Amps.
Converting these figures to "Power" (VA);
15 Amps x 240v = 3 600 VA (Watts) surge.
5 Amps x 240v = 1 200 VA (Watts) continuous.
Since you will not find an inverter with these exact "continuous" & "surge" ratings, you must buy an inverter that can accommodate the surge rating. ie you will need an inverter with a surge rating of no less than 3 600 VA for the above situation.
Other things to consider.
1] Many inverters use PWM (Pulse Width Modulation) to produce the alternating waveform. Electronic equipment does not like this kind of waveform & can be damaged by it. If possible, buy a "True Sine Wave" inverter...more expensive but better.
2] Generators naturally produce a "True Sine Wave", so you may consider keeping your genset & not buying an inverter.
3] The use of Deep Cycle batteries is recommended. No matter what type of batteries you choose to use, it his highly recommended that they not be discharged any more than about 50% of their total charge (DOD). If the inverter cannot give you info on instantaneous battery charge, you can use a Hydrometer to get this info. This maximum Depth Of Discharge (DOD) will ensure a much longer life expectancy from the batteries than if they were more deeply discharged.
4] You will need to calculate the amount of batteries needed against the size of the inverter (3 600 VA or 15 Amps) & the time you wish to run your equipment.
5] It is advisable that the inverter have a "built in" battery charger & other monitoring facilities.
5] It is advisable that the inverter have a "built in" battery equalisation process. (used only for battery banks).
6] The inverter supply MUST be totally separate from the normal house supply (this goes for generators too). This can be achieved by having separate power & lighting circuits or with the use of a "transfer switch". If separate circuits are used, it is recommended that the equipment NOT be earthed, unless required by the inverter system. Your electrician should know about this.
Other notes.
My calculations are based on the fridge & freezer starting currents being 4 times their run currents. In some cases, the starting currents of these devices are smaller than 4 times their run currents.
The sizes of the fridge/freezer used in the calculation are "typical" but you must still find the sizes of YOUR fridge/freezer.
A licensed electrician should make the necessary connections &/or changes to any circuitry/wiring.
You could use your generator to charge the batteries but I wouldn't recommend it as the inverters battery charger should have all the necessary battery monitoring devices & will be of a specific type to suit the batteries (usually "constant current" charging on the better inverters).
I advise that you do some reading on battery maintenance if you are going to use an inverter.