It depends on the type of barrel you have-- especially the previous contents, and the thickness/permeability of the wood.
I've had some good success using the following program to make a Flanders Red style beer, which I think is the most forgiving for a small barrel. First, a wood character isn't out of place in the style, and secondly, a *bit* of acetic acid is common.
1. Brew 5+ gallons of wort. Ferment with Roselare Blend in a primary.
2. After primary, put 3 gallons into your small barrel, and the remainder into glass (1 gallon jugs work great for this program. 3 gallon carboys are also useful)
3. While that beer is aging, brew another batch of 5 gallons. Either use Roselare, just Brett, or a clean ale yeast, it's your choice (there are pros and cons to each)
4. When you're ready to blend, you have 3 worts to select from. The barrel, the older non-barreled, and the newer, non-barreled. Determine your blend to taste and package the beer. Note: if you use only a clean ale yeast for step 3, or a brett-only beer that hasn't fermented out to the same FG as your Roselare blend, you could end up with bottle bombs. Either factor this in for your priming sugar, or put the whole blend into a carboy until the FG of the blend is stable. I haven't had too many problems doing this, but in theory, it could get very ugly.
5. The leftover non-barreled beer goes into the barrel, which you should have rinsed. If you have leftover barreled beer, put it in growlers/jugs.
6. Go back to step 3.
This ends up with a perpetual program of making sours without having to do a solera. I think of a solera as being more appropriate for larger barrels for a few reasons-- first, most homebrewers brew in multiples of 5 gallons. So if you are trying to do a 3 gallon solera, what will you do, brew 2 gallons? Secondly, with the small barrel, you have a lot more oxygen ingress, and for that reason, I believe that you want LESS contact time with the wood than with a large barrel. Whereas a solera maximizes contact time with the wood, at least for the oldest beer in the barrel. I would imagine after 1-2 years, the beer in a 3 gallon solera would be super acetic.