I was in a similar situation as you not too long ago; similar budget and similar decision. Rather than repeat a lot of the good advice that has already been presented, I will share my journey and maybe that can inform your decision even more. My interested in the Speedmaster is as the “Moonwatch” and the most interesting pieces to me are the ones with the strongest connections to NASA, spaceflight, and of course the Moon. For me, the vintage pieces with the strongest connections all used a 321 calibre movement and are all
well outside of the stated budget if you’re looking for something that doesn’t need much work.
CK2998 was the first Speedmaster to be worn in space in ‘62 onboard the Mercury-Atlas 8 “Sigma 7.”; it was Wally Schirra‘s personal watch The current generation “FOIS/First Omega in Space” is designed to look similar to that reference but with a more modern 1861 movement and is priced accessibly and within the budget.
105.003 was the only watch to survive James Ragan’s battery of tests that lead to the relationship between NASA and Omega with the Speemaster becoming officially certified for manned space missions in ‘65. This reference would be used in the Gemini missions and was worn by Ed White in the first ever NASA EVA. The current generation “Calibre 321” steel heritage model is based on this reference; still outside of the budget but all things considered not a bad price for what it is.
105.012 was the first to introduce the asymmetric case designed to protect the pushers and crown, the first to introduce the “Professional” distinction on the dial, and the first used in Apollo missions. Buzz Aldrin was the first to wear it on the Moon during Apollo 11. The newest 3861 is going to look the most like these externally, notably with the reintroduction of the stepped dial and DO90 bezel.
145.012 was the last to use the the 321 calibre movement and was also used in later Apollo missions.
With all of this into consideration, I chose to go with the new 3861 for now. They are easy to find within the budget and most closely aesthetically resemble the first watch worn on the Moon. A very close second for me would have been the 1861 FOIS. I generally prefer the cleaner dial and simpler case design. However, at the time that I was looking to acquire I stumbled across a deal on a 3861 here in the for sale forums that I couldn’t pass up. This lets me wear a watch that still has a lot of meaning to me that I don’t really have to worry about from the perspective of reliability. Now I can spend more time researching all of the nuances of the models above while I squirrel away money to replenish my watch budget. By the time I have enough to afford one of the more significant references I should be better equipped to discern a good deal from a bad one.