Generally speaking, modern integrated graphic cores should be enough to play many 1999 - 2010 games. There could are exceptions though like Crysis. Be aware that some old games may no longer be compatible with modern Windows. For example, Star Wars Knights of the Old Republic and the Sims 2 are not compatible with Windows 10.
From my own experience, I can say that a laptop with modern Intel CPU that has either a HD 620 or UHD 620 graphics core is sufficient to play the following games. This is based on using a laptop with a 4th generation Core i5-4200u and Intel HD 4400 that was released back in 2013. The Intel HD 620 is in 7th generation Intel CPUs. The Intel UHD 620 is in 8th generation Intel CPUs, but the UHD 620 is a very minor update to the HD 620. Improvements basically revolves around better support to playback 4k videos and a very small increase in clockspeed (100MHz ???).
- Mass Effect 1, 2 & 3
- Fallout 3 and Elder Scrolls IV: Oblivion - Needs the following graphics tweak file since those games do not recognize Intel integrated graphics cores. Both games use the same game engine developed for Oblivion.
- Elder Scrolls V: Skyrim - The Intel HD 620 / UHD 620 are fine for running that game with default settings at 1366x768 resolution. But with tweaks to the SkyrimPref.ini file and some mods to replace default textures smaller file size textures can allow the game to run at 1600x900 or even 1080p resolution with good results.
- Star Trek Online - Disabling the "Lighting 2.0" option (that was introduced into the game in March 2017), which makes graphics look "pretty", improves performance of the game. The Intel HD 620 / UHD 620 should have no problems playing the game a 1080p with this option disabled.
- Sims 3 - I don't play this game, but I have seen people play it on laptops with only integrated Intel graphics maybe around 4 or 5 years ago.
- League of Legends - I do not play this game, but there are videos that show that an Intel HD 620 graphics core is capable of playing the game on ultra settings (the game really has low requirements) at 1080p.
The least expensive laptop with an Intel HD 620 graphics core is the following Acer that has an i3-7100 for $350. It only has 4GB of RAM so it is highly recommended you install another 4GB of RAM (8GB in total) since all programs and integrated graphics will be using that RAM. It comes with a 1080p screen.
At $510 you can buy the following Asus laptop which has an 8th generation quad core i5-8250u CPU and integrated Intel UHD 620 graphics core. This is the first time Intel has released a "u" model CPU with 4 cores instead of only 2 cores. It has a 15.6" 1080p screen, but the thin bezels around the screen makes the size of this laptop closer to that of a 14" laptop. It has 8GB of RAM.
I generally recommend installing another stick of RAM (even if it is only 4GB). When it comes to integrated graphics if there is only 1 stick of RAM, the RAM operates at half speed rather than at full speed with two sticks of RAM. This can affect the performance of the integrated graphics core. Installing a 2nd stick of RAM can generally increase performance by 10% to 20% depending on the game.
The following 15.6" Acer laptop is the least expensive laptop with the nVidia mx150 graphics chip and is basically the least expensive laptop you will find with a dedicated graphics chip for $585. The nVidia mx150 is considered a mainstream GPU, but it's performance far exceeds the Intel HD / UHD 620. The laptop has a quad core i5-8250u CPU, 1080p screen 8GB of RAM and a 256GB SSD.