Lex, welcome. Yes, you should get a less expensive(than $3000)receiver; no, you shouldn't get "a cheaper AVR and use the pre-outs". A less expensive receiver, such as the Denon 4310 or Onkyo 3007, may very well fully satisfy your needs. Separate components continue to have a certain mystique about them, despite a lack of factual support. There's no magic that results from putting things in two or three boxes instead of one. The power needed depends on listening distance(more significant than simply room size)and sound level. Receivers such as those mentioned can drive Axioms to beyond safe listening levels in most home situations. In the unlikely event that more is actually needed, adding a separate amplifier can be considered at a later date.
The 4310 is available for around $1000 in factory refurbished form(eCost)and the 3007 for about the same(Accessories4less). These are likely to be at least as reliable as brand new units. Deals on new units are available(sometimes by calling)for maybe $200-$300 more from sources such as 6thAve, J&R, Onecall and Vanns.
