You didn't need to do that step,okay you did need to shut down the PC but the onboard would normally just disable itself when you have a PCI-E card inserted, unless the bios for your PC are setup very strangely, it won't be an issue though the only thing is if you ever run into issues with the graphics card and need to remove it you will probably see a low res 800x600 display on the onboard with the card removed now, no real issue if you have a net connection it will most likely just reget the driver just fine if you do need it again.

Fantastic news overall though, as for having unlimited fps (vsync turned off) know that runs the graphics card at 100% to draw as many frames as it possibly can, even though only a fraction of them will get displayed on your screen, I would normally just advise leaving Vsync on and your PC will run cooler because of it and you'll be able to have Minecraft running in a window and easily tab to other things like videos or so because Minecraft/or any game wont be trying to just use 100% of the gpu for the sake of it.

Your idea about the cpu is perfect btw, if you don't need to change out your guy for what you're doing, then don't, changing the CPU is tougher than slotting in a Graphics card to a port which is empty, it means having to remove the heatsink, remove the cpu which is in there and get the new one in there, termal pasted up and get your heatsink locked back on perfectly for it to work, like I said if everything is working perfectly for you now, don't put yourself through the headwreck for nothing.

If you are new to PC gaming btw could I recommend checking out the humble bundle site, every week or two they have a bundle of games you can pick up on the cheap, it works by donating an amount of cash to get the bundles, there is normally 3 levels of payment $1 gets you the steam keys for the base level games, paying 1c above the average paid amount gets you access to a bunch more titles and then they normally add a "give this amount to get X" which unlocks all tiers of the games they offer, really if you very few titles this is a great way to start to pick up a few good older games, often indie gems for a Steam account for yourself.

https://www.humblebundle.com/pc-android-14-bundle

https://www.humblebundle.com/store?hmb_campaign=DRMFreedomSale2016&hmb_source=banner&hmb_medium=banner

Also if you haven't already done so you should get yourself steam installed on that PC, they have a ton of good free to play titles there, even the only shooter of Team Fortress 2 is free to play now and a great little competitive classic team based shooter to enjoy.

http://store.steampowered.com/

Also of course there is blizzards gaming platform in Battle.net which has trials of a lot of games but does feature Heroes of the Storm and Hearthstone which are free to play

http://eu.battle.net/en/

And lastly from me you have probably heard of (for better or worse) League of Legends, one of the largest free to play titles out there, can be enjoyable but depending on the age of your Son I would be really slow to let him play this as the community can be very very mean (toxic) to others, especially new players and new people to online play could be very badly influenced by this poor spirited community.

http://na.leagueoflegends.com/

Just if you are installing these platforms know that they will all offer you the options to run these on startup (it's the default for most of them) so while going through the installer you'll wanna untick boxes that offer you that service since you're working off 4gb of ram you really don't want a lot of programs in the background which you're not currently using. (if you already have a bunch of things which open on start up can give me a shout to go through how to remove some of the unneeded ones from start up, it's an easy process to free up some memory)