Gordian III was followed by Philip I and II whose coins maintain similar grade silver. After that the quality goes down pretty steadily until partway through the time of Gallienus it was necessary to use a silver wash to make the things gray. This period from 238 to about 268 is interesting as you watch the silver disappear. There are many beautiful coins before and after but the 4rd century stuff is a popular place for modestly funded beginners to start. 4th century bronzes are cheaper yet just as the earlier material is more. We all pick what fits our desires and budgets. I do recommend that beginners stick to coins with decent detail that are easily identified and not try to save too much by buying things that are hard to tell what they are without more experience. Of your pair of Gordians, the nicer is easily worth 2-3x the other but I recommend the expenditure.
I've heard lemon juice works, but I haven't tried it. Better to get advice from someone with experience. The first thing you can do, however, is give it a long soak in distilled water. That might loosen some of the dirt, and it certainly won't damage the coin in any way.
If you know its pretty good silver, (which these were), you can try lemon juice. Just have some distilled water on hand and a clean soft towel. Soak in lemon juice until it lightens up as you want, then rinse in distilled water and pat dry. Then let air dry. NEVER, EVER use lemon juice on low quality silver like the mid 3rd century, or copper coins. The acid is too strong and can seriously ruin a coin.