I would like to comment on crew size. You only bring along as many crew as you think you are going to need to get stuff done. (More crew means more food, water, and messing/berthing space are going to be required. On a space ship, more cargo means more fuel or thrust required to go places.) As things get mechanized or automated, less actual monkeys with thumbs are needed.
HMS Victory (1778), roughly 230 feet long, 850 crew, 104 guns. (Sails, guns. Large crew is always a plus in boarding actions!) No automation or machinery at all. 6500 square yards of sail, 11 knots max. 3500 tons.
HMS Devastation (1873), roughly 307 feet long, 410 crew, 24 guns. (First British capital ship that completely dispensed with sails, although they will be used on other classes during the period.) 5600 HP from 8 boilers, 15 knots. 13000 tons.
HMS Majestic (1895), the classic late-Victorian age pre-dreadnought. 420 feet long, 670 crew, 40 guns. 10000 ihp, 16 knots. 16000 tons.
HMS Dreadnought (1906). 527 feet long, 800 crew, 37 guns. 23000 shp from 18 boilers for 21 knots, 21000 tons.
HMS Vanguard (1993, SSBN). 490 feet long, 135 crew, 4 torpedo tubes, 16 ballistic missile tubes. Nuclear reactor powering two turbines for 27500 shp, giving 30-ish (? classified) knots at a sprint, in a 16000 tons streamlined hull.
Remember, these are all warships, with weapons systems that need to be manned. (Low to moderate mechanization/automation.) Discovery is probably unarmed.