Can you install the plumbing fixtures (toilet, sink, shower) to a basement bathroom first and then install the walls and lineolum flooring a few years later for time and money purposes? What are the pros and cons to doing in this way and will this cause more work in the long run?

Lots more work except maybe flooring. Be very hard to install walls behind a shower, toilet and vanity once they are in place. I would go the other way, walls first then fixtures. . Vents need to go in before closing walls. Typical process is to rough in drainage and venting, install and finish walls and then install fixtures. What will support the shower walls and plumbing, it can't just hang there?

How about just doing the walls that are needed for the plumbing first and a tile floor later on instead of linoleum?

Before you start with the walls you should first locate the main and rough the job in, (see image) Run the water and vent and then install your walls, Good luck. Tom