I recently finished my first year of a PsyD program. I came straight in from my bachelors degree. I know students here who already have MA degrees in different fields, from clinical psych to social work to MFT to school psych. If you want to do a master's in clinical psych beforehand, I would highly recommend not doing one at a professional school. We have a master's program at my school and I feel like they do not do as high of levels of work as these programs at universities. The students I know with MSWs sometimes have discussed how different the two fields are, but I think it helped them when applying to practicum as they already had all that different knowledge and experience.
Be careful if you choose to do a masters first. Many of the students I know who did that found many of their credits did not transfer. My school offers an "acceleration" process where you cut off a year if you have a prior masters, but this is very intense. The students I know in it were taking 17/18 credits a semester while the rest of us were in 12. It's manageable, but a lot of work, especially if you could be admitted straight out of undergrad.