mgoedeke

My Recommendations would be if I understand your terminology correctly you have a 700 Watt base load and a 1.5KW peak load not KVA as that is calculated with a power factor..
So based on that premise you can do the calculations as follows 
Load 700 Watt runtime 4-6 hours lets work on 6 
6 x 700 watt =4200 watt this tells us you need a battery that can store and produce 4200 watt of useable power so the battery you can look at is a BSLB 6.4 KWH or a Hubble AM2 5.5 KWH the Bull has a theoretical capacity of 6400 watt @100% dod and the hubble 5500 watt @100% both batteries are 1C which means they can charge and discharge at their capacity 125 amp @ 48v for the Bull and 115 amp @ 48v for the Hubble you may use a little additional capacity for the peak load of 1.5KW but its negligible.
Now for the Choice of the inverter.. 
Your Continues load of 700W and peak of 1.5KW dictates a small inverter but will limit you to expanding your system so the recommend system and this is based on value for money is a 3KW Axpert clone inverter but they have a lot of limitations 1 MPPT limited solar power short warranty 2 to 3 years and they are basically designed as battery backup solutions or you Could look at a True Hybrid inverter like a Sunsynk Solis Kodak or Goodwe all are decent hybrids 5 year warranty  you scope or aim will dictate what you need also note any 3kw Axpert inverter is 24v and not worth wasting money on the Kodak 3KW Hybrid as an example is 48v and will work with the suggested batteries they also have duel 500v MPPTs which is more flexible however a 5KW Sunsynk is probably going to be your best choice.