Renstar what you are going to do is exactly what we did for all our 3 girls....and are backs are ok.
And your right, you dont need to spend anymore than $12 on a bath - it will do the job.

When baby does get bigger, those baby seat thingys that Jodi has posted are great. We also used one of those terry towling covered layback seats, that you pop in the big bath once they a bit older - they are under $20 in most baby shops....