One that offers decent gaming performance in current titles should be a cost-effective gaming machine (PC) and will last you a few years before you think about upgrading.
This will translate into a gaming PC that will now provide gaming experience with a high frame rate of 1080p and will provide playable gaming experience in the next 3-4 years.
Since the gaming industry is heading toward 4 K gaming, even for a budget-oriented PC, a decent 1080p gaming experience should not be a concern.
Given that we have chosen a slightly lower display resolution, both the GTX1060 and RX580 are decent low-cost GPU choices. A more future proof option will be GTX1070 or Vega56 if your budget allows it.
All current titles can be run by a quad-core CPU, so a Ryzen 3 1500X or I3 8350 is a decent budget-oriented option, while Ryzen 2600X or i5 8400 are more future-proof choices
Ram memory prices have dropped a bit, so depending on your budget, you can choose to get either 8 GB or 16 GB. For Ryzen, I must note that you should get at least 2933MHz certified memory, while the 2600MHz RAM modules are good enough for gaming with Intel.
You can choose a cheap motherboard to be cost efficient, but I would prefer one with Intel Ethernet and a newer audio solution like Realtek 1220 because you are gaming. A marginally better network response than cheap network adapters is offered by Intel Ethernet, and the only better alternative is a Killer Ethernet adapter. For instance, an Asus Strix B350-F is a budget option for Ryzen 2600X that can provide the above features but is relatively cheap because it is being replaced by B450.0.
Being cost-effective means that your case can bypass fancy led lighting, so having airflow is one important thing. For optimum airflow, get one that has a 12 cm fan in front and at the back, while the PSU is on the bottom of the case.
Finally, cost-effective means you may want to miss getting an SSD, but I highly recommend that you (and maybe one or two games) get at least 256 GB SATA SSD for the machine. Beware, for maximum efficiency, have at least 20 percent of the SSD empty. Those with slightly deeper pockets can choose an NVME M.2 512GB SSD with a 2TB hard drive configuration.
For hardcore gaming, laptop computers are not really suitable. Since their hardware is restricted to thermal and power requirements, they typically have variants of clocked desktop hardware. If possible, avoid buying a gaming laptop.