The university has framework agreements for buying computers, software, mobile phones; but also office and laboratory supplies. The agreements change in time and information might not be up to date in English, so it might be best to ask an Estonian-speaking colleague (e.g. someone from the department office) for specifics.
Some general guidelines:
Procurement of laptops, desktop computers, monitors, etc. and software: best to contact the IT Office through arvutiabi [ät] ut.ee. A glimpse of discount offers for the university can be found here (laptops) and here (desktop computers and monitors), but it is not mandatory to buy these exact models.
Mobile phones and other mobile data devices: the university has framework contracts, best to ask someone for the current specifics
Small office supplies: information available in Intranet
Laboratory chemicals and supplies: there are very many specific contracts, but the information is all in Estonian; besides asking a colleague, another option would be to contact the Head of the Procurement Office