Hi Scotsloon,
Hopefully this will help. Please note the whole thing was built from scrap wood scavenged from various places. I'm fortunate to have a charity-run wood recycling project nearby where I got most of the wood.
I never had any plans I just designed as I went, I think it is probably over-engineered and I might only use a single thickness of post at the top and bottom if I re-did it, but only if I had hardwood. I'd still do a double thickness if it was in softwood.
The protruding bits on the base are pointless, when I started the build I thought I'd be using some sort of turning mechanism to apply pressure, I worried the whole lot would topple over when the twisting pressure built up so I planned to put stabilisers on by attaching posts under them at a right angle. When I got the bottle jack it removed the need for them. At some point I'll saw them off.
The frame uses 7cm x 7cm hardwood posts (recycled from old pallets apparently) plus 2 pieces from a garden fence post. The pallet pieces are untreated wood but the fence posts have been pressure treated so I have only used those where they will not come in contact with pulp or juice.
I have a table saw so I was able to make the basket staves from another post, cutting out long strips and sawing them into 44cm lengths. The screws are stainless steel but if you look at the basket and juice tray you'll see there's never anything other than wood in contact with the pulp/juice. The big bolts are lengths of threaded rod cut to size.
The base
Top pic: 4 off 94 cm posts bolted to the ends of a bit of softwood fence post 44cm long.
Bottom pic: The platform made of 5 sections – lengths are 44 / 30 / 58 / 30 / 44cm. but I'd now do the 58 as a 44, much neater. Bolts through these to make a solid platform that slots down between the legs.
The top
Two 44cm lengths of post each bolted between the tops of the legs. Upper one is softwood again, but again out of contact with the pulp. The slots you can see in the legs were there when I bought the wood, they dont have any function.
The juice tray.
A square of 2.5cm thick plywood 30cm x 30cm. Sides are oak strips 2.5cm thick and 4cm high. Two are 30cm long, two are 25cm to fit between the longer ones. Glued to each other and to the base using PVA wood glue, and screwed tight while the glue dried to ensure a really tight waterproof joint. Again no metal exposed to juice. Afterwards excess glue scraped away with a chisel then the tray filled with a hot bleach solution for a while before using a scourer to really get the surface clean.
Drain: An angled 15mm hole drilled outward just cutting through the edge of the base to ensure there's no lip to stop juice running out freely, then a short piece of 15mm pipe to act as a spout pushed into the hole.
The basket
Tricky one in the end. The basket fits into the tray and sits on the bottom so the external dimensions are 25 x 25cm .
Top pic: Staves are roughly 2.2cm x 1.6cm and are 44cm long. The front and back panels are 25cm wide, ignoring the horizontal bars. The side panels are 21cm wide.

You'll see the bottom end of the staves have had a section cut out. This is roughly half the thickness of the stave and about 18mm high maximum. The notch must be on the outside of the basket. The reason for these is when the basket sits in the tray they leave a clear channel all the way around the basket for juice to run, This prevents the juice overflowing the edge of the tray. The edges of the tray are 4cm high so these notches are invisible in use but the top of the tray edge presses against the thicker part of the stave and supports it against the pressure of the pulp when used.

The horizontal bars are roughly 2 x 2cm and were deliberately kept too long while construction was underway because there was a lot of fiddling to try and get even spacing with evenish gaps. When I was happy I glued the staves to the horizontals with PVA and screwed them tight with s/s screws. After completing the sides I fitted them in the juice tray and then glued and screwed the horizontals to each other, then sawed the excess off the ends to tidy it up.
A net curtain serves as the pulp bag and I have 2 pressing plates made from the same 2.5cm ply as the base, these need to be about 1cm smaller than the inside of the basket so they don't get jammed. Short off-cuts of the posts about 15cm long provide blocks to put between the bottle jack and the pressure plate.
DRAWBACK : Unfortunately the release valve for the bottle jack is at the base, this quickly pushes down inside the basket and quickly goes out of reach which is why I use off-cuts between the jack and the pressure plate. Sadly the bottle jack does not work upside down
That was the first edition
After using it I found it didn't drain the middle of the bag of pulp very well so I made a false bottom of sorts to go inside the basket I had scavenged a few pallets from an industrial estate and one was made with hardwood planks so a plank was planed, and cut into 3 pieces to fit inside the base of the basket, then the table saw used to cut 5mm notches in a criss-cross pattern on the underside, then I drilled through all the crossing points and used a countersink bit to smooth the holes on the top. It works very nicely!

And the right way up part fitted in the press

What I'd do differently a second time:
1. I wouldn't have the sticky out bits in the base
2. I wouldn't have quite such a tall basket, it's just a bit awkward in use getting the pulp in and fiddling with the jack and so on.
3. I'd make the legs a bit longer underneath, The juice spout is only about 10cm off the ground so getting a bucket under it is a problem, I'm fortunate as I have a step outside the shed where I do the pressing and the press sits on the top step with the spout over the bottom step so I can get a saucepan under it ok.
Sorry for the enormous post!