No easy answers. There already are significant background checks in place when buying a gun. Go try and buy a gun and see for yourself.
How effective and complete are those background checks? There is probably room for improvement and better information sharing. But, much of that isn't as easy and "common sense" as many want to believe. Privacy concerns, equal rights issues, and practicality of enforcement, among other issues, are thorny problems to work through.
The only real "loophole" in the background check system is when a gun isn't sold, but given to someone or inherited...but even that has various levels of controls put on it in different jurisdictions, and really hasn't ever been at the heart of a mass shooting incident that I am aware of.
The bogeyman treatment of the NRA doesn't help either. Most of the invectives and conspiracy theories thrown their way is built on misinformation and ignorance. Any meaningful advances will require working together, so labeling gun owners as "nuts" and the NRA as a terrorist organization that doesn't care about school shootings is just super unproductive. Putting forward some half-baked proposal that is completely ignorant of current law, guns in general, or statistical evidence, and then getting mad when the NRA doesn't jump to accept it is not an indictment of the NRA or its willingness to work on issues related to gun violence.
I still think that medication is a major player in all of these mass shootings. I haven't seen with this Texas kid yet...but in every previous mass shooting of the last 20 years that I am aware of, the shooter was either on, or just recently had stopped taking, an SSRI drug. Every. Single. One. Unlike a connection with guns, the increase of these shootings correlates to the increase in use of these drugs very, very closely. I think this needs to be investigated much more closely. If there is an industry standing in the way of progress with effective background checks and psychological screenings, it isn't the gun industry nearly as much as major pharmaceutical interests.
Is there any actual evidence of this? I see it thrown around a lot by right wing blogger types, but haven't seen (and can't find) any actual stats/links to show it.