Well,
I still own two PCs with an OC AMD FX-60 @ 3,1 Ghz and a DFI LanParty NF4 SLI-DR with 4 GB of OC DDR1 as an ASUS A8N32 SLI Deluxe (with 16GB of DDR1..a little dirty secret few people know its possible).
I spent some time optimizing them (yes it plays Crysis ! ;-) so let's go steps by steps:
To put it short, yes your CPU and system memory are clearly the bottlenecks.
1) OS & Memory
Eliminating memory bottleneck is the easiest way to have a fast system.
You have chosen Win 10. Its the right and only choice if you want DX12 but issue is that the Athlon 64 doesn't support x64 for this OS (it's missing LAHF, SAHF, CMPXCHG16b as PrefetchW instructions which have been implemented first in 2005 Revision D).
This means you are stuck with x86 and losing about ~0.5G memory if you have installed 4G. Memory compression feature of Win 10 won't help enough and also use CPU cycles (but still faster than swapping with virtual memory).
Another point is that if your card allocates system memory in regards of its own memory size. So the bigger the memory of your GPU the less you have for the OS and the game.
Here I would go for win 7 x64 or win 8 x64 with 8GB (the CMPXCHG16b is only needed starting from win 8.1 x64).
2) Memory bandwidth
The Athlon 6000 has 2x1MB cache, this was fine in 2005 but is a limiting factor for today's code. So the next bottleneck will be your system memory bandwidth.
I do not know your motherboard and BIOS but if possible try to overclock your memory as much as possible. With DDR2 and Athlon's controller you should reach 6-8MB/s with T2 (test with sandra sisoft by example).
3) DX11 vs DX12
You want to go for DX12 (this is why you chose win 10), issue is that DX12 is more optimized for multi-threads than DX11 drivers which are almost running on a single thread. The AMD Athlon 6000 has two cores and is not optimal in this regard.
4) Memory card bandwidth & resolution
Ensure that your card is using PCIe 1.1 x16 and not x8 (can be tested with GPUZ). x16 1.1 is ok but x8 1.1. is too limiting (search for PCIe scaling if interested by this topic). Do not go over 1680x1050, load is becoming too heavy beyond that limit.
5) Memory card brand
Go for Nvidia, reason is that Nvidia's DX11 drivers have clearly less overhead than AMD's drivers, this saves you precious CPU cycles (PS I'm not religious and had over last 20 years as many AMD card than Nvidia cards).
6) HDD, SSD, RAM disk, cache...
Switch for an SSD if not already done, in combination with more RAM this will smooth your game-play. If you do not have a SSD but have more than 4GB but don't want to switch to an x64 OS try to allocate 2GB to a write back cache and a RAM disk for the virtual memory (there is a good article in tomshardware on this topic, in some cases you can keep your x86 OS but allocate the memory above 4GB to such utilities, no as efficient as x64 but better than nothing if you have more than 4GB (see
http://www.romexsoftware.com/).
7) CPU OC & idling unnecessary tasks during the game
You already did it.
Its fun maintaining these old PCs, Good luck !