A basement should be OK for running servers. Servers are very much akin to desktop PCs, with similar tolerances – thus if the environment is OK for people it's probably OK for computers.
For a home setup you probably don't need to worry too much about best practices (compared to what you will find in a data center), but as I don't know your basement environment best practices to bear in mind include:
The cooler the better – Data centers spend a lot of money cooling. From
a practical view, anything above 10 and under 30 degrees C is OK, with
18-20 degrees apparently being optimal. I'd have no qualms about running
my computers at anything above 7 degrees C.
Stability of temperature – I'd argue this is more important than temp
itself, as contraction and expansion due to heat changes are more likely
to shorten the lifespan of components.
Humidity – Too damp and you risk moisture on components and damage; too
dry and you risk damage from static buildup. About 40% humidity
is ideal, but most equipment will run between 5% and 95% humidity.
As for air quality, the cleaner the air the better – air clogs up fans which can cause servers to overheat (which makes them go slower) or die sooner (probably more a theoretical concern). If air quality is not great, you can schedule maintenance to clean out fans to overcome most of the issues here. Alternatively, filter the air before it's sucked through the fans – but you will probably need more/bigger/noisier fans to get the airflow through the filters.
I would consider retracting my close vote if the "can" questions were phrased in a way they don't seem like you are asking permission to do so. I relate "can" questions back to elementary school when kids ask "can I go use the restroom" and teachers respond "I don't know can you?" To give you a little push "What considerations ..." would be a good start of a title for the question(s) you are actually asking. Although I have a little hesitation to do so since I feel some answers could be highly subjective. – Ramhound – 2015-10-26T18:24:04.697
@Ramhound Thanks for the input, I see what you mean; how does it look now? – IQAndreas – 2015-10-26T18:34:36.193
1@Ramhound This seems to have become a pretty good question, I've voted to re-open. – misha256 – 2015-10-26T19:45:46.117
@IQAndreas - Yes; Your edits have turned several subjective questions into questions that can be answered based on verifiable facts. – Ramhound – 2015-10-26T19:54:50.097