The issue with a recommendation is it's unknown what the maximum load and duration of that load. The basis for sizing and installing an inverter isn't really that simple but from a safety perspective needs to be done correctly and per the book. If you do a search with my forum name you will find several installations and the basis for those. But to answer your question I would assume you are trying to simultaneously operate the listed appliances which is a very large load so mathematically lets say the microwave is 1500 watts, coffee maker is 600 watts and television is 25 watts which all together is 2125 watts. As these operate at 120 VAC that then is a current draw of 17.7 Amps. These loads are a combination of inductive and resistive but for simplicity let's use a power factor of 1. Let's go back to the energy required (2125 watts); inverters have an efficiency rating which is close to 90% then you want to keep below the maximum rated capability so another 10%. So the overall demand for sizing including inefficiency would be 2125 + 212.5 = 2337.5 + 233.8 = 2537.3 watts; therefore a 3000 Watt inverter would work just fine. So, the inverter's maximum battery demand at 12VDC will be right around 214 Amps. You can now calculate the DC cable sizing and fusing which is dependent upon the cable lengths. Now for battery bank sizing. Let's say you want a battery bank to support for 24 hours between recharging. Assume for this that the microwave will operate a total of 20 minutes per day the coffee maker 2 hours per day and the television for 3 hours per day. So for the microwave that is 1500 / 120 = 12.5 Amps then 20/60*12.5= 4.2 Amp Hours at 120VAC then at 12VDC is 42AH. Now for the coffee maker it is 100AH and television is 6.3AH for a total of 148.25AH then add the inverter inefficiency factor which brings the total to 163.1AH; let's say 163AH. Lead Acid batteries can only be discharged to 50% Depth Of Discharge without causing permanent damage; let's keep that at 40% DOD so you will have a long battery life and some margin. This means, for example, a battery with 100AH advertised capability that 40AH is useable. Therefore you can see for a daily use of 163AH between recharge you will need 4 each 100AH batteries connected in parallel. The next issue then becomes the recharge - for a bank this size and depleted as shown above the recharge time will be close to 4 hours to get to a proper float with a battery charger capable of providing between 60 and 100 amps current during the absorption phase; you will need a good battery monitor to know the state of charge.
