Snapper, My first Qs are;
1. You ask about charging your listed equipment in the bush, so what are your living in the bush arrangements? Tent, Camper, Caravan or other.........
2. Your listed equip.
minelab gpx detector battery, mobile phone and laptop computer The Minelab GPX has a cig socket charger, so can be done from 12VDC. Mobile phones are USB 5VDC charging, so can be done with a simple cig plug with inbuilt USB outlets as they transform 12VDC to 5VDC. Both the GPX battery and phones can be charged from your vehicle power sockets, whilst you drive and both are very low power draw so can be done whilst stationary from your main battery without risk of it being flattened.
3. The laptop is somewhat different, many run at between 16 and 20VDC (as well as other voltages). Mine is a Toshiba Satellite and it runs at 19VDC. Do you have a 12VDC laptop power supply or just the 240VAC they are supplied with? My laptop draws up to 2.0 Amps @ 240VAC, so that = 480W which means I need a 600W inverter, it would draw approx. 44 amps from a battery to do that. However I use a 12 VDC laptop power supply from Jaycar (see attached URL) it uses much less battery power to operate. If the laptop battery is fully charged it runs at about 3.0 amps, but if it is operating the laptop and charging a depleted laptop battery it is nearer 6.0 amps. But still much less AH to use than an inverter. It is also cheaper than buying an inverter.
https://www.jaycar.com.au/150w-car-laptop-power-supply/p/MP3472
The best method of working out how is;
1. As above, look at the simplest and least power required to do the charging of batteries. (as I explained all could be done from your car battery, but you would likely need to drive or start the car daily)
2. Next, employ another (Auxiliary) battery. If the only items are what you list, then a 50 AH is enough. However as mentioned in another answer, demand often increases. So a 100AH is probably the go. With output to a cig socket bucket or box containing Cig sockets, Merit socket, USB outlets and even an Anderson, you can literally connect almost any 12 or 5VDC item to it for charging or use.
3. The next thing is to look at how you charge the Auxiliary, the 3 main ways are;
a. from a small generator and a 240VAC smart charger. This requires you to carry these items and the fuel for the genny and only occurs when the genny is running.
b. from a DC to DC smart charger, such as a Redarc, Ctek or Projecta. This requires installing to your vehicle and only operates when the vehicle is running, but is much smaller than a genny, no extra fuel and much quieter.
c. Solar, this requires installing, a solar controller, needs to be deployed as standalone or fixed on the roof of the vehicle and only operates during the day. But no noise, no fuel and set and forget (other than managing use/charge).
All are budget driven and can be used independently or in conjunction with another or all 3. All have their pros and cons. Hope this helps