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How "fantastic" is the setting going to be? (aliens, hidden magic, ultra-high technology, improbable martial arts abilities, etc.)

That will factor in a lot as to what system to use. Remember, a system that is a Jack of all Trades is at best, may be superior in one or two specific areas compared to any other given RPG (and varying by comparison), but more often, is the not the best system for any application (i.e. the master of none).

Most RPGs tend to break down when applied to the modern era (1900s to early/mid-2000s), at least in a totally realistic setting. Players and GMs have enough experience with what does exist and what is plausible (and it's always the curious minds that tend to RPGs, so they're likely to spot such things) to drive military convoys through loopholes and logical disconnects in modern setting rules.

Spycraft 2.0 is good for a less fantastic setting with some fantastic elements (mostly plausible high tech)
Ninjas & Superspies is good for an over-the-top martial arts and high tech setting. One can also combine it (or use separately) Heroes Unlimited 2.0 or Beyond the Supernatural 2.0 for more skill choices, and more setting options (and BTS I believe has rules for normal people as well as the special types). Skill programs allow customization of characters, based on education, and even rules for going to school/training for additional skills beyond what's listed. The main failing of these Palladium games is lack of comprehension that some things are a lot tougher than SDC, even without using the MDC. Palladium also has the Compendium of Contemporary Weapons, which is actually a pretty good listing of common weapons for the time period you wish, and fairly convertable to most game systems.
(consider Spycraft an RPG for Bond and more cerebral things in the action genre, the Palladium games for Remo Williams, Indiana Jones and Hong Kong cinema)

HERO is prone to min-maxing and other manipulation the GM doesn't anticipating - not to mention rules interpretation (note that at least one edition of Champions had, in its credits, tag lines from the authors with their names, with one contributor saying "I can build GOD at 300 points..." and the next one replying in their tagline "...but I can prove it's illegal."). It has, at least in the editions I've played, a hard time dealing with the concept of personal weapons, making you pay for them with character points (as if they are powers), and having issues with other people picking up the weapons and using them, either as loaners, gifts or just prying them from the previous owner's cold, dead, hands. No clue what FRED is.

The generic version of D20 Modern, I've heard nothing but bad things about - even from people who contributed to it. I've heard better about systems that take it and modify it for their own settings almost to the point of unrecognizability, but those tend to be changes that best work in that specific setting.

GURPS is pretty good, but you got to make sure that your players understand which edition you're using, and what books (and skills in the books you are using) are just plain off-limits for use in character creation. But, in and of itself, it gives the greatest variablilty in what you can and cannot bring into a game. It tends to be a bit stiff in the larger scale stuff (like mecha and ship combat), but the RPG is one of the easier ones to use for characters that lends itself to conversion to let other RPGs' rules used for that macro stuff (like wargaming). Just make (or find) a system to equate "X" skill level in GURPS to a skill level in the other game, for wargaming and mecha combat apps, and you're set. Less varied, rarer but of similar use, would be the Tri-Tac games (Bureau 13, Fringeworthy, FTL 2448, etc.). I know one person who uses a mix of GURPS and Tri-Tac systems for characters and combat, and adds in parts of Palladium's games and West End's D6 system (derived from the original Star Wars RPG) for dealing with high-tech war machinery.