If you already have the system & have a limited budget, then you might as well see what you can upgrade on it.
From the owner's manual (http://downloads.dell.com/manuals/all-products/esuprt_desktop/esuprt_vostro_desktop/vostro-260_owner%27s%20manual_en-us.pdf), the 260 has a 300W PSU, & the 260S has a 250W PSU. Neither is going to be great, but they should be able to handle lower-power GPUs (i.e. ones that don't require PCIe power connectors). I would stick more with a GTX 1050 instead of the 1050TI,because a) it'll be a lot cheaper, b) the 1050TI is more powerful but not decidedly so for its cost, & c) it's a lot easier to find GTX 1050 cards that don't need PCIe power connectors. If you have the 260S with the lower PSU, you could also consider the GT 1030 (it only draws ~25W from the PSU).
CPU-wise, you're limited in 2 ways. First, as per the manual, your motherboard won't take Core i7 CPUs. Second, because the motherboard is only compatible with Intel HD 2000 graphics from the CPU, you can't use any Intel CPUs that use higher-level graphics. That means no Ivy Bridge CPUs, & even the i5-2500K is unavailable (as it has Intel HD 3000 graphics on it). That being said, you might be able to install an i5-2500 (the locked or non-"K" version). It's faster, it'll perform better (4C/4T CPU vs. a 2C/4T CPU), & it moves you from a 3rd-tier CPU to a 2nd-tier CPU (http://www.tomshardware.com/reviews/cpu-hierarchy,4312.html). It's not a great upgrade, but to be honest as a CPU it's actually not going to be too far behind Skylake or Kaby Lake Core i5s (probably on par with an i5-6500 or i5-7400 in performance).