I've used an FX5 filter on a 125G tank but it wasn't the only filter as I also had a used Eheim 2260. I'm a fan of having more than 1 filter on tanks over 75G for a couple reasons such as redundancy in case 1 fails and more filtration capacity plus circulation in the tank.
You could use an FX4 and a power filter (HOB) such as an Aquaclear 110 or any other brand canister you like and that is in your budget.
I've used the older Eheim/Jager heaters in tanks before but I really like the Hydor ETH external heater as the equipment is out of the aquarium though you are limited to using them out of the box with either 1/2" or 5/8" output fittings and compatible with similar canister filter hoses, so won't work with either model FX filter unless you DIY with additional PVC fittings and hose.
The new Oase Biomaster Thermo 600 canister filter is looking pretty good these days. A bit pricey, but the integrated 300 watt heater element built-in to that canister, is a very elegant solution to optimizing electric heating efficiency and keeping a (wonky looking?) submersible electric heater (visibly) out of the tank.
And, even though that canister filter would definitely provide more than enough biological filtration capacity for your aquarium... to provide redundancy, enhance water clarity and provide more flow/oxygenation of the water in the tank, a large capacity Hang On Back (HOB) filter is definitely recommended for use along with the canister.
A couple good choices to consider as the second filter for your tank, could be either the Aquaclear 110 or Tidal 110 HOB. The newer model Tidal 110 may have the slight edge, due to it's surface skimming capability.
I've got the FX6 on a 70 gallon mbuna aquarium set up. I'm generally happy with it although its noisier than I had imagined and have since heard some horror stories about the concertina type tubing developing pin prick holes - easier enough to swap out but more expense again.