You have other options too. There are kits that will screen for HIV, Hepatitis, Chlamydia and many other STIs. These are extremely reliable (and validated by the WHO) and are over 99% sensitive. They are reasonably easy to use, though you do need to read the instructions pretty carefully. It is controversial maybe, but in practice the most important is probably HIV because it is quite transmissible and whilst treatable remains incurable. Diseases like Gonorrhoea and Herpes tend to cause symptoms and in men visible lesions. Chlamydia is a problem because it is often asymptomatic and adversely affects fertility, so it may be worth testing for. I am not aware how frequently sperm donors have been found to have STIs – I suspect it is very rare in heterosexual donors, though obviously if you are considering a gay donor the risks are much higher.
For most people, the biggest problem is actually false positive tests. The chances of a true positive might be 0.1% or less if you are in a low risk group, and the chance of a false positive 1% (99% specificity is very good) this means you are 10times more likely to falsely test positive than to have a real positive – but it would still be pretty frightening.
Testing immediately before donation closes to the minimum the window for someone who has recently acquired an infection – otherwise how recent must a certificate be? A month? 3 months? A year?
However you look at it in the end it is a matter of trust, even if you go to a clinic. It must be a personal choice whether you prefer to subcontract that trust or whether you prefer to do things yourself and rely to a degree on your own instincts.
Through a clinic I am not sure you get much more information than race and hair colour – it may vary from clinic to clinic but that is all the people I know have been told.
I hope this is informative.