Take a look at
http://colegun.com/ Cole's is the East Coast Beretta specialist and can custom build a gun to your specs. Gil
My experiences with Coles have been very good, but their custom guns start around $6k, so they would not fit this budget.
My first OU was a Franchi Alcione - used, they can be had for $1k or even a little less and you would be hard pressed to find a better gun for that price. The entry level Guerini (Woodlander) is about $3k new, which is $1k more than the 686 Beretta SP1 or White Onyx. The Guerini will be a bit better finished, have much better customer service (assuming you need it) and has three free clean/overhauls. Long, pointless debates could be had about which shoots better and will last longer. Both are good guns - the Beretta will probably hold value better on resale. I haven't spent much time with B. Rizzinis but my understanding is that their entry level guns are a good value compared to Guerinis (very similar actions, with less finish). CSMC just terminated their relationship with B. Rizzini - not sure who is servicing those guns now.
Guerini is working on bringing out some new OUs through Fabarm as a result their recent investment. If your need is not immediate, you might want to wait to see how that plays out.
Going OT here, but a gunsmith recently told me recently that Beretta was having their lower end guns made in Turkey now.