So I went ahead and re-watched the episodes. There's various bits that do seem to imply the ships are quite empty, but there are several instances of hiding from patrols and SG1 get captured twice (once only two of them) though they do break out too.
Within the Serpent's Grasp
They arrive in a cargo hold, dark, with an unguarded but active stargate in it, steal weapons from the crates. It's implied they're using the gate to ship supplies through onto the ship.
11:00 Some guards come in, SG1 hides behind the crates.
14:12 SG1 move through the ship's corridors, using as much cover as possible. All corridors appear dark and relatively uninhabited. (Ship on night-cylce?)
14:49 They actually just walk up to Klorel's sarcophagus while he's in it. This is later said to be the bridge.
15:49 Hammond prepares to send SG3 and the other marine teams to 'arrest' SG1 'officially' for court martial. It's pretty obvious he means for them to act as reinforcements mission though.
16:43 A guard enters the bridge, SG1 kill him, vapourise him.
18:40 SG1 relocate themselves.
19:20 SG1 hide from a patrol of ten serpent guards and at least four un-helped jaffa.
19:30 They sneak into the hangar deck. Jaffa priestesses walk past with Klorel's sarcophagus.
20:30 SG1 follow them to a meeting in the stargate chamber, various military and 'civilian' personnel are seen. SG1 just sneak in the back and hide behind the crates. The jaffa then leave.
23:20 SG1 plan to kidnap Klorel. Teal'c says "They do not know we are aboard, there would be little reason to keep him aboard."
23:45 The team attack the goa'uld ship's bridge, three guards with Klorel. Teal'c advises O'Neill to lock the doors, then shoots the lock for both doors.
26:30 Sam & Daniel hide from a patrol of eight serpent guards in a corridor, approaching the hangar bay. Plant explosives on one of the death gliders.
28:00 Jaffa attempt to override/repair the lock, others physically work on opening the door, while serpent guards stand by to enter the room.
29:30 Jaffa break through the doors, surround Jack & Teal'c.
31:20 Klorel brings Teal'c and Daniel as prisoners to the stargate chamber to present them to Apophis' hologram. Apophis asks how many more came with them, O'Neill claims 'thousands' Klorel says 'I assure you father there can be no more' when Apophis orders a painful excecution for Teal'c and orders O'Neill killed however Klorel pleases.
33:50 Klorel/Skaara orders the priests and guards to hold off on the excecution, and take Teal'c and Jack back to the bridge.
35:40 The ship drops out of lightspeed somewhere past Saturn.
36:40 Daniel and Sam hide from a a large group of Serpent Guard and Jaffa, then tail them to the hangar bay, where they man the death gliders.
38:28 Daniel and Sam duck out of the way of a couple of guards leaving the bridge, distract more with a smoke cannister, along with Jack and Teal'c they overcome the guards, kill Skaraa.
41:09 The ship approaches Earth, Earth and the Moon are visible.
The Serpent's Lair
01:37 Jack says "we should expect some of their reinforcements through that door any second." Sam says that she'd set a 24 hour time delay on the explosives they'd been planting, as of this point, they prepare to detonate manually.
02:20 Guards arrive and begin to crowbar the doors, throw in a flash grenade, capture SG1.
04:45 SG1 wake up still blinded in a cell. "We've been in worse situations" Everyone disagreed.
05:40 Daniel "Right now they're getting ready to wipe out the major cities of Earth. They'll do it from orbit, out of reach."
07:00 Bra'tac chews out the former leader of the jaffa onboard (has he come over from Apophis' ship?) and executes the guy. He puts Klorel in the sarcophagus.
07:50 Major Samuels claims they'd not be in this situation if they'd buried the stargate. Hammond doesn't seem impressed.
08:50 Bra'tac rings over to Apophis' ship, reports on what has happened and assures Apophis that he's put Klorel in his sarcophagus. Apophis orders Bra'tac to excecute SG1, Bra'tac says he'll do it himself.
10:00 Samuels' goa'uld buster plan with the gigaton warheads, been discussed before.
11:25 Bra'tac enters the prison cell, Jack and Teal'c, punches Jack in the face and decks him, then starts chewing them out again. God I love that guy.
13:00 The ships have been in orbit for eighteen hours. It seems like a goa'uld shock grenade can make people unconcious for many hours, or that that's how long the sarcophagus might take to deal with chest wounds from a 9mm.
15:00 Bra'tac gives the group back their weapons, in the Stargate Chamber. Scene linked above.
19:24 The C4 is now 41m from detonation.
23:17 SG1 encounters two guards, kills them..
24:22 Apophis orders Klorel to burn the first city on Earth down to the ground (would be interesting to know the target).
24:50 Bra'tac claims "There are sentries in every corridor." Presumably around the bridge.
25:30 Bra'tac beats two sentries up.
27:00 Bra'tac goes in first with the a rebel jaffa (the serpent guard with him), creates a diversion by blaspheming Klorel.
28:11 SG1 and the two other rebel jaffa attacks, guards begin coming in from elsewhere, Daniel mortally wounded (he gets better). They take Klorel with them to use as a human shield briefly. We only see two of the rebel jaffa killed, but presumably the serpent guard dies too, unless he was killed in friendly fire there.
30:10 SG1 beam over to Apophis' ship, holding Klorel as a hostage, which causes Apophis to order them to hold their fire, run out of there and shoot the locks. This is one of the scenes that always made me believe the claim Daniel makes one time that goa'uld don't feel familial love. If Apophis didn't care for Klorel in an emotional way, he'd just shoot through him and put them in the sarcophagus again.
31:00 They make it un-challenged to the top of the shield generator, destroy it with grenades.
33:30 They use a goa'uld shock-grenade to take out the maintenance personnel in Apophis' ship's glider bay and steal grenades.
34:45 Daniel is revived, and escapes by stargate. Apophis and Klorel escape by ring transporter presumably to a smaller ship hyperspace or by going through the stargate after Daniel.
I'm not sure how many soldiers one could conclude were aboard from that.
I know also from later episodes that crews of 1000 (ha'tak) and 2000 (unknown class) are given for goa'uld capital ships, by Teal'c and Ba'al respectively, while we once scaled the ships at 650 m or so and production art gave them a maximum width of 1km.