Here is a link to a complete parts book for your 350.
Official Case IH Online Parts Store and Case IH Catalog for Best Parts Search and Best Parts Look Up. Case IH Parts for Case IH Tractors, Case IH Combines, Case IH Tractors, Case IH Manuals, Case IH Parts
And here is a link showing an exploded view of you shift mechanism, with part numbers, and description to the right.
Official Case IH Online Parts Store and Case IH Catalog for Best Parts Search and Best Parts Look Up. Case IH Parts for Case IH Tractors, Case IH Combines, Case IH Tractors, Case IH Manuals, Case IH Parts
I would at least find an I&T manual to get started. They aren't the best at describing some procedures, but are better than nothing. The IH Blue Ribbon Manuals are top of the line, and can't be beat. Best bet to find them, would be on ebay. The bad thing is, they come in a sectional manual for each assembly. The complete manual may be 4 inches, or more thick, but doubt you'll need the whole thing, because the I&T has a lot of the tune-up info, etc., condensed. You can save a search on ebay, and when something comes up you can use, and is in your price range, nab it..!!