Hi,
Since you want it to be portable, you must use SMPS technology. You have to switch 4 sets of MOSFETs in full-bridge configuration at high frequency and use a ferrite transformer for stepping up the voltage and then convert this to DC. Then you must switch 4 more sets of MOSFETs/IGBTs at 50/60Hz to convert the high voltage DC to AC. You can use quasi-sine output and for pure sine wave, it would be best to use microcontroller and SPWM.
Do you want just an inverter or battery charger as well? I think you'll need battery charger. So, design a charger based on full-bridge configuration controlled by a PWM chip and again using ferrite transformer. You should implement current/voltage limiting to avoid damage to the battery and you have to set charging current depending on your desired charging time.
Then you need protection schemes such as low-battery protection, overload/short-circuit protection, etc.
These are just the basics. You will need a lot of effort from here on in to finish your project. Research on each of the sections to gain more idea. You need to have a good background of electronics to catch on.
Hope this helps.
Tahmid.