How many men did Duke Leto have on Arrakis?

In brief, we don't know. It seems like Frank Herbert never bothered much with that clarification as there's no mention of Atreides troop numbers in his novels.

Some estimation has been done elsewhere, based on Hawat's assumptions about the likely number of troops that could be used against them

The best hint is this:

"We don't have much time, as you well know. They'll be here with Sardaukar disguised as Harkonnens at the first opportunity. How many do you think they'll ship in, Thufir?"

"Four or five battalions all told, Sire. No more. Guild troop-transport costs being what they are."

"Then five battalions of Fremen plus our own forces ought to do it. Let us have a few captive Sardaukar to parade in front of the Landsraad Council and matters will be much different—profits or no profits."

And Thufir's later reflection:

For a full attack they'd expected no more than ten brigades.

We're told that an Imperial brigade is about 3,000 men. The strength of a battalion is never given, but in our world it apparently ranges between 300–1,000 men. So Hawat's first estimate is somewhere in the 1,200–5,000 range, while his second is 30,000. Presumably his first "all told" number must only be counting the Sardaukar, while the second is the full Harkonnen force he expected. (Or it's an inconsistency.)

Given that the Atreides troops are supposed to be within a hair as good as the Sardaukar, that a Sardaukar is supposed to be a match for 10 regular conscripts, that they know the Fremen are formidable fighters (although they may not realize they're already almost a match for the Sardaukar), and that the Atreides apparently felt relatively confident of winning such a confrontation—but only with Fremen help—I would conclude that the Atreides troop strength on Arrakis matched:

The expected Sardaukar force (4–5 battalions) = 1,200–5,000

Plus one tenth of the expected Harkonnen force of 30,000 men = 3,000

Plus a bit, but not very much, more, say = 1,000–2,000

(To be reinforced by 4–5 Fremen battalions)

So probably somewhere in the range of 5,000 to 10,000 Atreides fighting men. That should be enough to give them a clear advantage in the attack they expected, while not enough that it wouldn't pose a genuine threat.

As you can see, this calculation depends heavily on an assumption that the Atreides troops are very superior to Harkonnen troops one-to-one. If this assumption does not hold, we might be talking 30,000 Atreides troops or more.

When I read the first book, I always thought there were no more than a thousand men. I guess I just couldn't comprehend the hugeness of this world and the Atreides per se.

As I carried on, though, I felt like the Atreides was so much bigger. I did some research--the encyclopedia, the books themselves, the wiki page, etc.

I've come to the conclusion that there were 100,000 men at most prior to the Sardaukar assault. They were incredibly outnumbered. And as we know it, there were around 300,000 Sardaukar troops on Arrakis.

More specific to your initial question on the troop numbers there are no definite tables but 300,000 seems reasonable for a planet of no more than a few million.

There is a large expense to sending men across space and battles often devolve to hand to hand combat, this is also in the future where most individual powers have parity as far as technology. Meaning everyone can be pretty confident in the performance of their forces and troop numbers.

An army of 300,000 men dug in would probably be more than enough troops for any opponent. With the exception of an opponent + imperial sardaukar.