Sea-Fastening and Pad-Eyes

Sounds like you are starting from scratch, here. What are you building? Specifications change as the years go by, and new metallurgical/corrosion knowledge is gained, but for an off-the-wall example Bridges typically use(d) ASTM grade A36 steel exhibiting a yield strength of about 36,000 lbs/in².

If you're referring-to structures such as offshore steel platforms associated with oil & gas production, the API Pecommended Practice RP-2A(WSD) ...{Working Stress Design}... provides a wealth of such knowledge, while heavily referencing the AWS D1.1 Structural Welding Code for attachment specifics. Anything "structural" in the offshore realm will mandate full-penetration welding (no fillet welds, and absolutely no skip/intermittent welds!). These documents can be bought online.

If you're referring to Ships, drilling rigs and such,
visit the American Bureau of Shipping's site:
http://www.eagle.org/ (click "Rules and Guides" at the top, then "Common Structural Rules")
this will take you to:
http://www.eagle.org/prodserv/applications/csr/index.html
where you can download demo software.

As far as how thick or stiff a given pad-eye should be, that depends on it's purpose. Those used simply for hanging appurtenances are much smaller (and less 'stiffness required') than those at the top of an offshore platform's legs, used for lowering it to the seafloor, and then lifting it back out again.

Hope this helps at least somewhat... Best wishes ~