Look at real-world ship plans and adapt them? It's the best way to ensure realism. Or for fictional ships, if you insist, see if you can find Spelljammer ship plans. It's fantasy, not sci-fi, but they may provide some inspiration.

That said, intuition suggests that a ship carrying all that stuff would be mostly cargo and hangar space, with engines at the aft end, big doors at the prow, and living quarters tacked on to every side. And it would still be painfully cramped. Real world ships invariably are, even large ones, and a spaceship has even more overhead in the way of conduits, cables, pumps and whatnot.

Alternatively, maybe something not unlike the Space Shuttle would make sense? It would still be mostly hangar space.

Depends on the level of 'hardness' of sci-fi you are working with.

E.g. did anyone care that travelling a 30 tons spaceship across the Solar system in 4 hours would take almost 100 tons of deiterium/tritium (or He3-H) fuel and even more in contemporary H-Li system? I.e. a 'normal' interplanetary (not even intersteelar) constant-acceleration ship (i.e. a military ship) would be 80% made of fuel storage in case of fusion drives. While drifting spaceships thou travelling slower will require less fuel respectively. The numbers will be better with antimatter fuel or any other fictional 'high-capacity energy storage method', which at contemporary understanding of physics caps at m0c^2 (i.e. it may shrink the size, but not the mass).

On the contrary, you may choose to alter the laws of physics (e.g. to overcome the lightspeed speed limit, inertia laws), then your ship will be build around the specific technological means which will define its form, size, weight etc. Maybe you would not be needing any engines or fuel in that case.

In case you need to make a holywood-style spaceship, it doesn't need fuel at all, but definately an unsafe nuclear reactor and a small gym :)

My advice is to sketch it out, even if it's on a napkin. See if it makes sense, if it works for the verse you're going for, and tweak it until it does.

You might want to look up real ship plans and design principles. Otherwise, just go with what feels right until you get something you like.

im looking for a way to literally put it on paper. i have no artistic skills.

Um, straightedge and pencil? How else? You said you tried graph paper and the scale was too small. So, increase the scale? Use bigger paper? Learn the basics of technical drawing? There aren't any shortcuts.

Alternatively, there are numerous applications for drawing game maps out there, and any decent one should support floor plans as well. See if one of them works for you. AutoRealm used to be the best, but that was long ago. Look around.

Hmm... if you do not care about realism, so the task is rather simple. You just have to set minimal sizes for every unit of your list.
150 m long x 20 m wide x 20 m high (approximately according to the 'clay model' you give)
In non-realistic setting you'd station decsk 'along' the ship, as navy ships do, not perpendicular as acceleration force requires. Then each deck is roughly 4 m high. Let it be 3.5 m plus 0.5 m for armor and technical supply equipment. You get 5 decks x 20 m x 150 m = 3000 square meters x 5 decks = 15 000 sq.m. of space. Multiplied by 3.5 you get 52500 cubic meters of the ship interior.

Let's think now about the interior.

Modern reactors are large (core 25 m long and around 20 m wide). And safe non-explosive reactor models (e.g. a travelling wave reactor) are even larger (core up to 60 m long, around 20 m wide). That would take all the ships rear.

So the ship interior will instantly drop to 120m long and we get 12000m2 and 42000m3 respectively.

Crew quarters must contain roughly 50 people. With ceiling height of 3.5 m a two-storey bed of 2m x (1m+1m free space) is applicabble, resulting in 2 square meters per a crew member living space requirement. So you get 100 sq.m for crew quarters. Let the gym be half of it. 10 Showers/bathroom would roughly be 10x4 sq.m. = 40 sq.m. Leave at least 0.2 m as a wall between rooms. Plus captain quarters larger than that for others, let it be 10 sq.m.

Water tanks must contain water for 2 days it is (in ~realistic) 50x2litresx2days = 200 litres or 0.2m3. Water filtration facility may be very small.

Escape pods must be capable of containing 50 crew members. I.e. each has at least 1m2 per man, that is about 4x15m2. Now add armor, flight control, engines for each escape pods. So, each would then take about double that amount so, reserve 4x30m2 space. The escape pods may be rather large in height (let it be 5x6x4m), so its dock would stretch two decs high including additional equipment and facilities, so each escape pod dock would take 30m2 for the pod, additional 30m2 for equipment and maintenance space around x 2 decks = 120 m2.

Medical facilities must host at least half of the crew simultaneously, but better all of them cramped on double-stored beds. So its the same as living quarters space - 100sq.m.

We're left with roughly 11000m2. Now for the cargo.

2 hummer/warthog like transports dock would be roughly half of escape pod dock i.e. 60m2

1-2 heavy vehicles seem the same size to me, so their dock would take another 60m2

2 small/light fighters would be twice the escape pod size i.e. they take 240 m2 each = 500m2 dock.

2 heavy/larger fighters would be three times larger than the previous, would take 3 decks and resulting space requirement 1500 m2 for 2.

2 drop ships are even larger, let them be twice than the previous, so 3000 m2 for two is enough for both.

So... we're left with 6000 m2 of space.

We cannot specify sizes of the main battery, oxygen scrubbers, armory, cargo hold, communications, galley, food storage, cooling and heating, stealth drive core, cloaking device, main shield generator, hydraulic dropping floor as we do not know what technologies they require. Maybe some of them, like stealth device, shield generator should be 2 or 3 decks high.

I.e. we just take all the remaining space and share it between them (12 units listed here). i.e. approximately 500m2 each.

the engines and the primary weapon system are located outside the ship's decks.

What's the next step? Depends.

You may take a 5 sheets of paper and try to draw everything on them with a pencil and eraser. Or, cut a colored paper into pieces of the respective size (i.e. in scale 2mm = 1m you would get an A4) and try to play with moving them around. When you are satisfied with the result, you draw it with ink. Then you look at the plan and then finally re-draw it clean.

Came up with another idea - determine which parts of the ship are plot/mechanics-important. I.e. which should be detalized. e.g. if you would like to walk around the ship, then its all the rooms you have access to. If the player spends most of his time in the living quarters, you should make them large. If you need to calculate ship systems damage and crew fatalities depending on attack angle, the systems should be simple and not detalized, just some approximate space. And if you need it just for decoration/ship upgrades visualization, it is absolutely arbitrary how you place the ship elements and which size they are, they just should be large enough to see the difference between 'crew quarters' and 'ultra-comfortable crew quarters' / 'cloaking device mk1' and 'cloaking device mk2', etc.

(UPD) HEY!!! We've forgotten the most important part of the ship - the SELF DESTRUCT BUTTON. Should reserve at least a 1m2 for it, because it is usually large. :D