I've been an engineer for 20 years and I have started remodeling my house (1959) two years ago.
The master bath was tops on my list. I wanted a whole new bathroom. Bravely I began the demolition process, swinging my hammer enthusicastically at the ugly grey 4" tiles and prying them loose with a crowbar. I did pretty good for a while. Got most of the floor tile and wall tile out and some of the linen closet. Removing the floor of the shower proved beyond my ability. Also, I could take things apart but putting the new stuff in was waaaay beyond my abilities. Now, the UGLY part...The bathroom sat in this condition for a year until I found the right person for the job.
I found him doing some work for a neighbor and hired him to finish the demolition (probably saved myself about $500-800 for what I did do) and to do the whole bath remodel. My baths are small about 6' x 7'.) And I bought and picked up all the materials myself (had the heavy stuff delivered, like the cast iron tub) and all I paid him for was labor. He subcontracted the plumbing out (and that was included in his price.)
I had some estimates from reputable remodeling contractors. I feel that by the work that I did (some demo and buying and gophering all the materials) and by using a self-employed "handyman" I got the whole job done for a few thousand less. Not bad. (Caveat, there is some risk in the handyman approach..not all are good, honest or reliable. Go visit the last job they did.) It did surprise me how expensive a bathroom remodel really is, even a small one.
And the bathroom turned out GREAT!
My other bath just needed the wall hung sink replaced with a vanity and sink and new facet and mirror above it and light. I tackled all of these myself and they look great also.
I would leave any major wall construction, shower or tub construction, or behind wall plunbing or electrical (other than lighting) to the professionals.
Even with my success, there are some things that are not quite the way a pro would have done; like my mirror needs more glue behind it (...on my to do list) and my faucet wiggles a bit (..on my to do list) and you have to invest in tools you never heard of like a faucet wrench to reach way back up under the sink to tighten the faucet washers.)
Just sharing..hopefully some food for thought. Good luck whatever you do!