You want an efficient cheap reactor with no additional chambers, or a good breeder? Sorry but I just don't see that happening. any efficient design is going to have to spend so long turned off to cool with 1 chamber it would be better to just build solar panels until you can afford a full reactor.
I am talking relative efficiency. the cheapest reactor you could build would have 2 individual uranium surrounded by water. sure, that uses minimal resources ignoring uranium, but it has the worst possible efficiency. The design offered above is a good example of what I am talking about, but also note that a mk 2 is also acceptable, and if the cooling-heating ratio is close enough for an exceedingly simple redstone circuit to control on/off time, even mark 3. just don't let components melt. As for breeders, I haven't gotten a chance to fully test it or upload it but if my math is right its a 3 core breeder that you heat as a mark 4 and then run at ~6000 heat with redstone turning it on and off so the net heat by the time it finishes doesnt spawn lava.