Unfortunately, there's no job that can be played well with just 7 buttons in raid or EX trials content.
However, there are jobs that can be played...less than optimally...with only 7 buttons. If you do that though you risk raising the ire of your team mates so you should probably stick to doing 4 person content, such as dungeons, with a party of your friends.
As you've noticed, it is possible to play a ranged version of RDM with 7 buttons. DNC and Bard can also be semi-effective with 7 buttons. Monk and Nin won't be possible. SAM and DRG could be played with 7 buttons but you'll never be able to build to your strong hits so you'll always feel kinda weak.
WAR, PLD, and DRK all have short main rotations but they also have a lot of cool downs and party responsibility. If you go in with a healer who knows you won't be using your CDs then you may be able to do one of these. GNB will have too many buttons for you though.
I would avoid healers. They require a lot of cooldown management and party awareness, more so than tanks do.
Overall, I think you'd be best helped by finding a good FC that can help teach you and go through content with you. They would also be the best way for you to approach more demanding content.
If you choose to do crafting and gathering, you'll still be required to get one job to 80 so you can get through the MSQ and unlock all zones but you may have an easier time with those jobs. You don't have to worry about quick decisions and you can always read the tool tips at your leisure if you forget what a skill does. Gathering only uses a few skills at any given time and crafting is easily done with macros; even without macros you don't use that many different skills for each craft.