You can certainly get a nice usable vintage Leica for $500 or less. However, you need to understand a few things before you choose one. Leitz made two different systems of 35mm rangefinder cameras. The earlier system has a mount that accepts lenses that screw into the camera body (what we call 39mm screw mount, or LTM for Leica thread mount). They introduced this system in 1930 with the Leica I (C) model, and continued it well into the 1950's up to the classic Leica IIIg. Concurrently during the 1950's, Leitz introduced a new system that accepts lenses with a special bayonet mount (rather than screw in, the lens is placed against the mount lined up with a red dot and a quick quarter turn locks it in place).
This is known as the M bayonet system, which started with the superb Leica M3 and continues right up to the latest M8. Okay, for $500 you want to find a classic Leica that your fiance', who probably knows and appreciates the Leica mystique, can enjoy in his free time. I'm talking hobby camera, not camera for his work, because a photojournalist today would be doing his job with the latest digital gear. No problem. You're on the right track looking at the Leica IIIf.
On the 31st of August, 1846, I left Concord in Massachusetts for Bangor and the backwoods of Maine,... I proposed to make excursions to mount Ktaadn, the second highest mountain in New England, about thirty miles distant, and to some of the lakes of the Penobscot, either alone or with such company as I might pick up there.
—Henry David Thoreau (1817–1862)
It's a common model, with over 180,000 sold between 1950 and 1957, it accepts all the zillions of screw mount lenses Leitz made up to that time (and also early 39mm screw mount Canon, Nikon, and even many Russian made lenses), and there's always a bunch available on eBay. I do not recommend the Leica IIIg; although it is a better camera, collectors keep it's price hovering in the $1000 range. I do not recommend some other common earlier models like the Leica III, IIIa, or IIIc; although they're equally common and readily available for less money, they are also just old enough to cause a lot of trouble and frustration. Among the screw mount models, the Leica IIIf is a great choice. Find one that work! Don't take a risk on an example that needs any sort of repair. Look for one that has a bit of external personality (as long as there's no overt damage, a few rub marks or gentle dings are not a problem), the seller guarantees it all works, as it should. And the Leitz Summitry is a fine fast lens, but get the Elmer 5cm f3.5 instead if you can.
Forget the original box (collectors will PUSH the price for original boxes, but there's no advantage for you there), don't worry about a case (they fall apart, and they sometimes cause more damage to the camera because they hold in moisture), but do try to get a proper Leitz lens cap. This is your best bet for a usable vintage Leica in the $400-$500 range. Now if you want to bend just a bit, and you'd like to explore those later M series cameras, you can probably get a 1960-ish Leica M2 with a superb Submicron 50mm f2 lens somewhere in the $500-$600 range. All the same thoughts apply in regards to condition, etc. The biggest advantage of the M series over the old screw mount series is that if your fiance' eventually wants to get a modern Leica (for work AND pleasure), any lenses he already has with the M2 would be interchangeable with the later camera. The classic M3 is too desirable among collectors, the M1 has limited features, and you could consider stepping up for the M4 (actually it would have to specifically be the M4-2 because the original M4 has become quite collectible as well), but that model is the first of the "modern" designs. So there you have it, the Leica IIIf or the Leica M2, those are your best choices in your price range.
A damsel with a dulcimer
In a vision once I saw:
It was an Abyssinian maid.
And on her dulcimer she played,
Singing of mount Abora.
Could I revive within me
Her symphony and song,
To such a deep delight ‘twould win me,
That with music loud and long,
I would build that dome in air,
That sunny dome! those caves of ice!
And all who heard should see them there,
And all should cry, Beware! Beware!
His flashing eyes, his floating hair!
Weave a circle round him thrice,
And close your eyes with holy dread,
For he on honey-dew hath fed,
And drunk the milk of Paradise.
—Samuel Taylor Coleridge (1772–1834)
Regarding your question about Leica values, in general, yes, all of them do increase in value. The vast majority increases slightly ahead of inflation (over time, not right away), so not that terribly high, but certainly enough to equal money in the bank (and assuming you deal only in top condition). The historically significant models, and a few choice rare models, increase by much greater degrees, in some cases to the point of being ridiculous. Common models like the IIIf just seem to float along with the economy. So, in general, leica cameras appear to be a good to excellent "investment".