I saw that it can be classified both as an analytic and a synthetic langauage, so which one is it?
A language can be both “analytic” and “synthetic”, the two categories are the polar points in the analytic–synthetic spectrum (or call it ‘continuum’) on which you position languages, that's why some languages are more analytic than others, or one can say, for example, that language X is synthetic with a some analytic features, but its related language Y, while being also synthetic, has a greater degree of analyticity.
Welsh is inflectional (not isolating), synthetic with analytic features. If you know which features are which, you can yourself measure the proportion in which synthesis and analysis are represented in Welsh, you've just got to conduct a little statistics research using any grammar of Welsh.
Welsh is inflectional since Welsh words can be modified in order to mark grammatical categories on them, while isolating languages don't modify words for grammar categories. For example, Welsh nouns can be modified for number with a suffix:
afal “apple” – afalau “apples”
or even with a sound alternation inside the root which is a characteristic synthetic feature:
fford “road” – ffyrdd “roads”
On the other hand, the Welsh definite article is a separate word, which is an analytic feature:
tân “fire” – y tân “the fire” (cf. Romanian, where it's a suffix: om “man” – omul “the man”)
but when the article comes before a feminine noun, the first consonant of the noun undergoes a mutation, which is a synthetic feature:
tref “town” – y dref “the town”
As all the Celtic languages, Welsh widely uses the word-initial consonant mutations, very synthetic of her. For example, only by the mutations one can tell “her” from “his” in Welsh, since both of them are ei, but each causes a different kind of mutation:
calon “heart” – ei galon “his heart” – ei chalon “her heart”
Welsh verbs have lots of analytic forms, very much like English, and the modern spoken Welsh uses them very often, much more often than the Literary Welsh language — spoken Welsh is simpler and more analytical than Literary Welsh. That's the general tendency among the Indo-European languages of Europe: although very synthetic originally, every century they are getting more and more analytic.
"Analytic" and "synthetic" are ends of a continuum regarding morphological versus syntactic means of combining elements, where "more morphology" is on the synthetic end and "more syntax" is on the analytic end. Since a language can use both syntax and morphology to combine elements, and languages do both, a language isn't strictly one or the other. Ideally, one could compute an index of morphological complexity for any language, though it is unclear exactly what you would count. Supposing that you simply count the number of non-lexical affixes (including "processes" such as reduplication), the next question is where the dividing line lies. You could try answering the question by randomly sampling 100 languages and finding the median affix count for languages, though this runs into the problem that most human languages fall in the Niger-Congo and Austronesian phyla.
Another approach is to sample the literature to see if most linguists who use the terms call Welsh "analytic" or "synthetic". The problem is that there are further terms such as "isolating", "inflectional", "polysynthetic", "agglutinative", "fusional". Wikipedia has collected a list of claimed analytic languages which includes English and Scandinavian, but the page on synthesis also lists examples of English as examples of synthesis. Since English and Scandinavian are taken to be architypical analytic languages, one might compute "morphological complexity" for those languages vs. Welsh and see where Welsh lies.