Couple of points:

1. The “stem ends in い” rule for spotting group one verbs is not hard-and-fast – there’s always exceptions. 見ます (みます), to give an example, is group two. Another way to define the groups is that all group two verbs have dictionary forms ending in る (which is why they’re also called る-verbs) but again there’s exceptions. For example, 作る (つくる) is group one (which, incidentally, are also called う-verbs).

2. する compound verbs are always Noun+する – this rule is one of the exceptions to the “every rule has exceptions” rule. 勉強 (べんきょう) is a noun, meaning “study”. Generally it’s going to be two or more kanji before you reach the する/します while group one verbs ending in す tend to only have one. Without kanji, you’ll notice nouns tend to be four kana long (often with glides), while verb stems are usually only two or three, and never have glides.

3. Without kanji to help you along, or if the kanji just isn’t helping, then it’s really just a matter of remembering them case-by-case, or getting good enough to intuit it. Maybe try sounding it out, to see if it sounds a little silly.

I noted the part about する verbs being based on nouns, but unless I already knew the noun it was going to be hard!

Well then, what does that tell you? Learn more vocab, of course :D When you’re at a beginner level, it’s not really essential to be able to predict anything, so don’t worry about “How can I tell this or that just by looking at it?”. If it’s an ambiguous case – or something else you’re not sure of – look it up, don’t be frustrated that you can’t guess it straight away; like Joel says, you’ll develop an intuition for certain things over time.