I couldnt see the tank in the link for some reason, but if its the one I'm thinking it is, I've heard great reviews on it, and actually bought it for myself but ended up returning it after finding a better deal.
As for your tap vs. spring water dillema. I'd ease into tap water slowly. Using spring in a 5 gallon tank would be expensive over time! Just get like 4 gallons instead of 5 one week, then 3 the next, and so on so forth....that'd ease him into it slow enough.
You should definitely get a heater and thermometer. a 25watt adjustable would suffice, 50watt is recommended. (eheim jager, or hydor theo are highly recommended. I love my Theos!) You will be very surprised by how much more active he becomes.
As for the filter, if its on low he should be okay, but if you notice him getting pushed around by it a little too much then remove it, and if you still want a filter switch to a sponge filter, which has practically no output but still has enough area on it for you to cycle your tank.