Since you're steady on your position i'll simply go on and help you upgrade, without reiterating anymore my stance.
E7500 is not the absolute best you can buy, but imo, in the perspective of upgrading the whole system with a 100-150$ budget, it would be a nice upgrade for almost 0 money. If you wish to go over your budget of a bit, then the Q9650 is the best between the two. I'd stick with the E7500 though, since in a future perspective, you'd need to throw away both of them. It would be more wise to invest your budget in upgrades you could keep.
DDR2 is the memory your mobo uses, i've referred to the link you first posted here: https://support.hp.com/us-en/document/c01287561
I don't know what type of memory you're currently using, since speccy says DDR2-333 but your hp link says another thing. Anyway, it's DDR2 100%, but you may want to further look into this, to avoid buying another ram stick you can't use along with yours.
4 GB is the maximum you can get, as usual for old mobo. I've found out looking for your mobo specs from the link you gave us: https://support.hp.com/us-en/document/c01357119
If you're going to add a dedicated GPU, even if it's a GT710, you may want to look for a new PSU, since yours it's a (very) old 250W with no certification, which could likely fail soon. PSU is another thing you could transfer to your new build in the future, so i would go for it.
There is a good deal on this good PSU: https://www.bhphotovideo.com/c/product/1001257-REG/evga_100_b1_0500_kr_500w_80plus_bronze_power.html
which basically will make it cost 19.99$ with free shipping
This is the overall upgrade: https://pcpartpicker.com/list/RxMwq4
If you wish to spend the full budget, i'd upgrade the SSD and go for a 480GB one, which is currently around 30$ more.
In that project there are 2 RAM sticks, since i don't know what's your ram, except for the fact that is a DDR2. If it turns out to be DDR2 800, you'd need only one, otherwise, for 10$, i'd say buy both sticks.
EDIT: I don't know about investing the budget for a 1050 or a 750TI. They're both huge improvement over your system, but you need to buy a new PSU for both and with your cpu, even with the 7500, you risk to bottleneck it.
EDIT2: I've seen you've found good deals for the 1050, in that case it's worth to upgrade.
Edited by hamluis, 15 July 2018 - 10:27 AM.