Hi what do you want your computer to do anyway? From your previous specifications of your old computer, the GPU won't be transferable to your new build unless you use the old motherboard which won't be the case since you are asking what new motherboard to get. THe AMD HD 7570 has a video card rating of about 1000 so you should shoot for an upgrade twice that and the price range I see for older cards in that range would be similar to the GTX 550 Ti. Only get the old version or older architecture video cards that are rated 2000 and above for two reasons. Your cpu is no longer ideal for graphics especially gaming so any significant purchase in the video card department will only be bottlenecked by the cpu in performance. This may be more apparent if you play cpu intensive games such as DOOM or CS GO. I don't suggest you spend over 50 dollars for a card.
I don't know if you should gamble spending money on getting older video cards or an expensive motherboard since the restricting factor will be your cpu.
Make a list of what you need the motherboard to do before you pick one. Can you only live with 2 ram slots or do you need 4? Make sure the slots are all the same ram slots and not designed for 2 different ram types such as DDR2, DDR3, or DDR4.
Don't consider overclocking because it's not worth it because your cpu, ram, or video card will bottleneck the performance anyway. Buying a video card or any peripheral needs to consider if you can use the old 300W PSU you have or do you need to get a more powerful one to be able to use other add on cards to your system. I am assuming you are going with your old 300W HP PSU.
Don't consider any motherboard over 100 dollars because that's not reasonable for the budget build but if a mother board can be obtained below 100 dollars then you can consider it but not above that price range. Make sure whatever board you pick that you locate the internal speaker connector and make sure that part works because it will tell you if something is wrong with the system when you finally turn the computer on.
Do you have all the connection features that you want on the motherboard? Too many means you are wasting money on features you will never use.
Are you going to use legacy parts? The newer motherboards don't have DDR2 ram slots, SCSI or parallel port connections, etc. The older boards don't have USB 3.1, NVME, PCIE, SATA3, Wifi, etc. I don't know what you want, have, are going to use or are willing to buy to adapt. You probably need a new hard drive since old hard drives may not be able to be formatted to use Windows 10. Try to use your old operating system in the new computer but it may not work because the old OS may be intentionally bound to the old hardware. If you have to buy, you can get a new Windows 10 OS for around 20 dollars on the internet and download the OS to your new system.
The GIGABYTE GA-F2A68HM-H FM2+ seems okay if you can get the latest revision and can tolerate the limitations. Please check the reviews for problems people have faced. But I cannot recommend any FM2 motherboard because I have no experience with those boards to be wary. I am assuming that your budget to build a new computer is only 100 to 300 dollars and not higher than that. Also I think you also want to use old parts from you old computer so my suggestions are not about other alternatives to get a better pc.