As no one else has yet posted, here is something to think about.

If you want to talk about different kinds of swords available in the middle ages, check out the Oakeshott typology. This is a recent attempt to organize 11th to 16th century sword types by physical appearance. Different forms were prevalent in different times.

I would challenge your implied premise that an infantryman would have necessarily used a sword at all. The medieval period is broad, and infantrymen in your qualifications could vary from pre-Norman theigns to 15th century dismounted french knights neither of whom would necessarily use a sword as a first choice in battle. /r/askhistorians has had a few posts about the commonness of swords, like this thread.

Consider the prevalence of other weapons, like the war hammer my personal favorite. /u/TheJucheisLoose gave a really phenomenal answer there.

Also check out these threads: http://www.reddit.com/r/AskHistorians/comments/194wc1/why_did_the_soldiers_in_your_area_of_study_use/ http://www.reddit.com/r/AskHistorians/comments/x1upz/just_how_prevalent_were_axes_flails_and_other/ http://www.reddit.com/r/AskHistorians/comments/1w4gbt/why_did_knights_still_use_swords_after_the/

While I am always glad to receive any questions about the Middle Ages, this will be a very difficult one to answer with any specifics. It would help immensely if we could dial it in. A region and a time period would make the task much easier. A Byzantine Tagma soldier in 950 is going to be equipped very differently than an Anglo-Norman levy spearman in 1130.