I've got a #4 Flypress and have built a table (incomplete) for it.  The legs are 4 X 3/8 Square tube welded to 3X2X1/4 channel between them.   The unattached top is a piece of 3/4" plate that I plan to bolt to the  legs.  Was thinking of using 1/2 inch countersunk bolts, but was wondering if I should go larger, like 3/4-inch.  I tend to overbuild things, and was curious what this group felt about bolt size for the table?  I look forward to the discussion and thank everyone in advance for their response.

There are three words that are critical to keep in mind when designing the base for a fly press: overbuild, overbuild, and overbuild. A fly press exerts an enormous amount of torque when it hits the bottom of its stroke, and the bigger the press, the greater this force will be. You want the bolts to be as big as possible, the frame to have as much diagonal bracing as possible, and as the whole set up to have as much mass as possible.

I have a small flypress (unfortunately the number on it doesn't appear to correspond to standard rating system, so can't tell exactly how large).  It came with the manufacturer's CI table, so I can't directly comment on that other than to say that your legs sound heavy enough, but the assemblage needs to be configured and assembled in a way that will resist the torque load that Jon mentioned.  Gussets and cross-bracing will help with this.

As far as the lag bolts go, I used 1/2" with lead inserts to tie mine down to my concrete slab.  I expect that these will be most challenged by a shear load, so I selected grade 8 bolts for the purpose.  Your press is likely larger than mine, so I don't think you can go wrong with larger bolts, but a lot will depend on the floor type and the eventual weight of the table (which will also function to absorb some of the torque load).

My press is about the same size as Latticino's, and while it's not bolted to the floor, I did build up the base to hold about 400 pounds of sand as ballast. It helps.

First, thank you for the comments and I understand about overbuild.  Let me give you more of an idea of the table size.  The table by itself weighs over 500 pounds (the top plate is 48x32 and weighs around 330 pounds by itself), so it actually weighs more than the press.  The table does have cross bracing plus 2X2X1/4 angle iron welded to the legs around the bottom to support a piece of 3/8 plate for a shelf, so the legs are welded together top and bottom all the way around.  I plan on using 3 countersunk bolts per side for a total of 12 bolts for the top.  The shear strength of a 1/2-inch Grade 8 bolt is just shy of 30,000 pounds - if I were to jump to 5/8", the shear strength jumps to approximately 46,000 pounds, and if I go to 3/4" bolts, around 66,000 lbs.  As the press will be bolted to the top plate, the bolts will be sucking up a lot of the torque load, so I was wondering about the size.  I want it bolted so I can take it apart should I have to move it (which I don't want to do, but you never know).  I plan on using bolts long enough to go completely through the nuts by at least 2 threads so I have full thread engagement and the maximum pullout restraint.

Sounds pretty good. How many bolt holes in the press? What do you think of drilling and tapping the table? A couple drops of locktite takes the place of nuts and lock washers or fiber lock nuts on the far side. It will also allow less lateral deflection than long bolts even in snug holes. 

I seriously doubt you want grade 8 bolts, they don't have nearly as much stretch so require much higher torque to hold like they should. Remember, you're bolting down a casting you don't want to split an ear. I've been happy with grade 5 bolts, I've hammered 1/2" G5s with my impact wrench till it was chattering (stalled) without shearing the heads to prove a point. If working loose is a concern paint a match mark on the bolt heads, just a tiny stripe between bolt head and the press foot etc. if a bolt moves you can see it clearly. Yes?

If you're concern is the press torquing and going walk about  on the table, weld some stops to the table in contact with the press's feet that way all the bolts really need do is keep it from jumping. Short say 1" pieces of 3/8" sq. should be more than enough. Say 2 each. on the outside of each corner at 90* to each other. Bracket the corners from the outside and it can't go anywhere. The stops will take any lateral torque stresses and will be a large indicator if something gave, they'll move obviously. Yes?

Put "hips" on the table legs, diagonal members from the table to the legs at the lower shelf. So long as the shelf isn't very high off the floor, say 1/3 total leg length, you don't need hips between shelf and the end of the legs.

The shape of strength in structures is the triangle. A square can hinge on opposing or parallel corners and give. A triangle has no hinge points, tension or compression on a triangle means 2 sides are under one and the 3rd element under the other force. Any movement means crushing or snapping of one element of the triangle. Take a look at a steel trestle bridges and you'll see the elements make triangles or are tied together at corners by diagonals which make 2 triangles.

The stock you list is plenty strong with a little "structural" construction you could park a dump truck on it. Your fly press MIGHT make is slid on the floor but the table and legs won't move.

Bounce any questions off me and we'll refine the details.

 Frosty The Lucky.