An easy-to-identify willow is the almond willow Salix triandra - it has a characteristic `jizz`, with a quite twiggy branch structure, smallish glossy mid-green leaves and flaking bark. It is not a native but is planted occasionally as part of landscaping schemes, as in the photos below from the Pwll section of the Millennium Coastal Park, Llanelli. In Carmarthenshire, it is also occasionally encountered elsewhere, as it was once grown - along with other willows - for basketry; hence it occurring at Pontnewydd in the Lower Gwendraeth Valley and a stand that, until recently, grew where the main coast road now is, on the coastal flats east of Morfa, Llanelli.
It is a small willow and always floriferous - making it perhaps suitable for a wild garden and, like all willows (except the native S.cinerea and S. caprea), it is easily propagated from cuttings. The density of flowers (note that it has three stamens per floret, hence the specific epiphet `triandra`) must surely also make it a good moth lure early in the season.
About twenty years or so ago, I undertook much recording of willows in Carmarthenshire to assist George Hutchinson (then of NMW). George subsequently published the results in the Llanelli Naturalists Bulletin:
Hutchinson, G. (1996) - Salix (willows) in Carmarthenshire: a guide to identification. Llanelli Naturalists Bulletin 2:23-33.
[includes some brief notes on distribution in Carms and actually includes a very high proportion of the willow taxa found in Wales, with photocopies of typical leaves etc, so also very useful for vc41]