My cousin had one of those Mamaroo "swings" that has a hanging mobile and a whole variety of movement patterns/speeds/vibrations vs. a traditional swing. It takes less room than a regular old-style swing and it can be set on a table if you're vigilant. They're expensive but look for a hand-me-down or on Craigslist. http://www.toysrus.com/buy/portable-swing/4moms-mamaroo-c...
I think you can do without a tub if you're pressed for space - use a thick towel in the sink, and once the baby is sitting, I thought a tub ring was great. Now I've seen people put a bigger child (9 months-2 years) in a regular laundry basket set into the tub - the water goes through the holes, the 4 sides keep the baby contained, and a few toys fit inside and don't float away. I didn't do a lot of bath toys - tupperware, funnel, colander worked great until age 3.
I agree about the changing table being unnecessary - I was always changing my kid on the pad in the diaper bag or on a towel.
We never used a walker much - they kept bumping into things like doorways and chairs, and my son was on his feet at 8 months and running at 9, so it was useless for us.
But I do see what people are saying about things helping you keep your sanity even if you only use them for 4-6 weeks. What we need is a "lending library" for equipment that you sign out and return in a month, just like a library book! A friend of mine lives in co-housing, where people share large kitchen equipment, yard tools, hardware/tools, and a large community room for parties or holiday dinners. There's a certain logic to that