Clearly I'll need to learn a little more about GURPS then.
Edit: My first thoughts on Gurps: I have to buy books to figure out what it is? No. Okay, so looking at Wikipedia you apparently only get four attributes and some other stuff. That's pretty simple I guess, I don't know if it'd necessarily be better though.
I'm an experienced player, so I can give some basic info:
GURPS exclusively uses six-sided dice for everything, and almost all rolls are simply done with 3d6. You have four attributes: Strength, Dexterity, Intelligence, and Health. Along with the obvious things that they affect, these stats also determine your starting HP, FP, basic speed (essentially your reflexes) and basic move (how fast you can run), Will, Perception, and so on.
GURPS is a point-based system: the GM selects how many character points the players start with, and you use those points to build a character. Increasing beyond average costs points, while decreasing gives points back. There are also Advantages, which give you various benefits or abilities (like Combat Reflexes or 360 Degree Vision), and Disadvantages, which confer penalties or flaws to the character (like everyone's favorite, Alcoholism, or Hemophilia). Most GMs set a limit to how many Disadvantages you can have or how many points you can get back from them, as most Disadvantages give the player anywhere from 5 to 20 points to spend; limiting Disadvantages prevents minmaxing.
Skills are likewise purchased with points. Each skill has an attribute that corresponds to it and a difficulty level. How many points you put into a skill determines how much it's trained based on the defining attribute. For instance, a DX/Easy skill (like Guns) requires 1 point to bring the skill level to equal your DX, so if you have 10 DX you get a 10 in Guns if you put one point into it. More difficult skills require more points for each level, and characters with low attributes have an inherent disadvantage in the relevant skills.
GURPS is different from d20 in that low rolls are better. To make a skill roll, you roll 3d6 and try to get at or below the target number. A 3 is always a critical success and an 18 is always a critical failure; your skill level and sometimes equipment affect whether the crit range for successes and fails increases past those. This means that unlike d20 and such, roll probability is on a bell curve: rolls in the middle of the range (from 8 to 13) are the most likely to occur, with very good or very bad ones being less and less probable.
GURPS is a completely universal roleplaying system, and as such the Basic Set only provides the absolute basics to set up most common campaigns. Sourcebooks provide much more detail, and they tend to go into so much detail that they can actually be used as reference material for non-GURPS stuff. High-Tech is the go-to book for anything taking place from the industrial revolution onward, Low-Tech for cavemen up through the renaissance, and Ultra-Tech for sci-fi.
It often gets accused of being math-heavy, but it's really not. There's obscene amounts of optional rules for both realistic and cinematic gameplay, but these are optional; the best thing about GURPS is that it's designed to be 100% modular, and you can literally strip it down all the way to a pamphlet that fits in your back pocket. You can freely add or remove rules, including house rules, and you're usually safe. All of the units are real-world measurements rather than abstract game units and equipment is given stats based on heavy research (the formula for determining firearm damage is still being parsed out, but it's very complex and tends to create results almost identical to the real world), which means that making custom items and weapons tends to be fairly easy just by comparing stats to similar stuff already in the book.
GURPS shines when used for realism and in many ways is built as standard for realistic games, but there's a ton of cinematic rules and sourcebooks that allow for stupidly wacky games with about as much realism as the average B action movie.
Edit: Looking at your suggested house rules, GURPS would work quite well for it. You don't have "classes", since you just buy everything from the ground up, but the books often provide templates that can be used as a basis for characters. Having to make everything from square one instead of being restricted to classes also really helps with flexibility, and you can make much more varied and useful characters and expand them naturally as they progress.