I agree SMTnet is the better forum to ask. However I think you need to include further detail. What defects/deviations from spec are you able to pickup from what is presumably a visual inspection that enables you to determine they are not reaching IPC Class 3?
You cannot expect to simply buy a line and magically achieve your quality goals. If your 3rd party is not achieving it, there is probably a reason, it takes some to and fro between manufacturing and design to make sure both the PCB and process is setup in such a way your standards can readily be met. If that time and effort isn't put in with your assembler they will have one arm tied behind their back when trying to meet your goals, this may be exacerbated by your small batch sizes which might encourage both parties to not have sacrificial trial runs, budget in expected failures or tune in the layout of the board and stencil design.
I'd probably pick equipment that can talk to each other easily (i.e the SPI can feedback to the printer etc). As Loki says any major brand of pick and place should be able to work to Class 3. Perhaps for belt and braces accuracy, Id' focus on models that either measure placement force and/or measure the component height/coplanarity. Europlacer gets a good look in here (look at its videos placing on warped boards) but entry level machines from the bigger brands often don't get these features.
he same goes for the printer, but here you need to understand all your boards/panels and their support needs in the printer, getting this right is key to a good print. I have put quite a bit of time and effort recently into comparing printers, SJ Innotech are highly regarded but didn't really apply to my requirements, I don't think you can make a bad choice, however EKRA might be another nice option to look at. MPM are crazy money (at least in the UK) more than double a nice DEK or Europlacer (Speedprint).
I'd be inclined to disagree on the "any mainstream oven" however, if you are targeting Class3, there is presumably a reason and many of the industries or applications that require it also have requirements like low voiding. This requires both careful selection of you flux chemistries but also a good reflow process. I'd suggest you probably want Nitrogen and vacuum in a convection oven to best optimise here. However given the volumes, it would be way more energy efficient to use a batch Vapor Phase system with Vacuum, something like the Asscon VP810 Vacuum.
3D AXI is the dream, but you might find better value in a 3D AOI plus a manual X-ray process focused on points of interest (I've never priced AXI but I think its possible to get pretty close to Lokis suggested 2nd user AXI cost with new AOI+MXI)
5 Personel seems like radical overkill, you might run a team this size to keep a high speed SMT line fully occupied for maximum ROI on the equipment(kitting jobs, refilling feeders and minimising downtime) but you are talking about 25 boards in a day, something somebody should be able to do single handed or with an assistant/supervisor for verification + your THT board stuffers.