Instrumental Music
Handel was principally a vocal composer, and thus the rather small section. However, he did write some notable instrumental pieces that should be staples for any orchestra that cares about stellar Baroque music. Below is a serviceable summary. You will note that it begins by addressing an all-too-common association with the composer.
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The Water Music
If the worst injustice done to Handel is the ignoring of the oratorios, the second place prize would go to the peculiar fame of the Water Music. Despite the thousands of recordings of it out there, and its frequent inclusion in compilations, it is perhaps the least interesting music Handel wrote in his entire 50+ year career. In spite of a nice movement or two, it basically caters to people who want their classical music to be unobtrusive background noise and not require their attention.
Bottom line: he wrote far better, so do not judge him by this one.
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Music for the Royal Fireworks
Commonly yoked with the Water Music, I prefer this unusual grandiose concerto any day. It was written for outdoor performance, and thus makes use of horns and trumpets. The music is not the most complex, but it is certainly spirited and meant to be enjoyed for its own sake. The first movement (by far the highlight) is among Handel's best works, and the rest is worth a hearing or two.
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The Great Concertos (op. 3 & 6)
Now we get to the good stuff. Between the opus 3 and opus 6, we have 18 concertos that are first rate, but which do not require extravagant forces to perform. Most consist of 4 or 5 movements, usually alternating between fast and slow. In the fast movements Handel demonstrates his skill with counterpoint, while the slow interludes show the eloquence and expressiveness that made him so great at writing for solo singers.
I endorse these two set of concertos highly. Possibly the best instrumental music he wrote, and a fine contribution to the genre of the Baroque concerto.
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Organ Concertos
Again there are two sets, opus 4 and opus 7. The majority of these were composed for interludes in oratorio performances. Handel was hailed as a spectacular keyboard virtuoso by his contemporaries, especially on the organ. Much of the appeal of these concertos would have rested on the improvisation and embellishments that Handel himself added. Quite a shame we cannot hear these, but the pieces are quite beautiful and noble as we have them.
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Trio Sonatas
Some nice chamber music on a smaller scale than the Opus 3 & 6 mentioned above. Monica Huggett of the PBO has made a recording of them with the Sonnerie Trio.
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Solo Instruments
Handel wrote the occasional suite or sonata for a solo instrument (violin, flute, harpsichord) but none are considered among his most important works. And the good movements they do contain were probably used elsewhere to make a superior aria or chorus. Bottom line: all are respectable pieces, but not the most vital, so hear the others first.