This is a familiar situation for many of us. Do I hire someone to do this job or do it myself? Either way, there is a sub-decision about the approach. Let's consider that sub-decision first.

Replacing the old tile can be done with either traditional tile approach or one of several kinds of pre-fabricated tub surrounds. 

I talked to a couple of companies who install the latter, and the prices were up in the "pretty scary" range. As a general rule of thumb, the better the pre-fabricated surrounds are, the more expensive they are. Some of them are really, really good-looking. Some others, alas, look like trailer park stuff. For the ones in the price range that I would be willing to consider (up to about US$1000), I read a lot of online reviews. Some people said they were fantastic, and some people wished they had never heard of them. Par for the course in product reviews. My subjective conclusion was that satisfaction might depend on the skills of the installer. I was a little unsure about how well I could do it. I didn't want to spend that money and have something that had ragged edges or wobbly walls or whatever. Having something like this professionally installed was out of my cheapskate budget range, and lack of confidence ruled out trying it myself. So, pre-fabricated tub surrounds were off the table.

For a traditional tile job, the question revolved around how good a job I might be able to do myself. I've had an itch to do some tile work ever since I saw it done over and over on home improvement shows like "Hometime" or the early years of "This Old House". These days, most of those shows are about how to hire a contractor, but years ago they used to actually show you how to DIY stuff. Anyhow, they made tiling look pretty easy, and they were always able to finish it within the 30-60 minutes of the show. Wow. I never had the time or real reason to do any tiling until now. The open question was: would it look like crap and beg to be ripped out, or would it pass aesthetic and functional muster? 

For the functional part, my plan was to over-engineer with belt and suspenders (more on that later). For the aesthetic part, there is some artistry involved. I was afraid of the usual DIY finding: by the time you are done with the job, you have enough experience to do a good job on the next one, but the first one you did might be a bit raggedy. 

I decided to do a trial. It would take some investment, which would be a complete waste if I decided I had to hire someone, but would be a minor outlay if I decided to go ahead with DIY. I selected a wall in our unfinished basement that is out of the way enough that a train-wreck tile experiment would be recoverable. I made a few tentative decisions about materials and used exactly those to tile a couple of short rows of tile on that wall.

As you can tell from the photo, I wasn't completely careful about edges and things. I wanted to see if I could get things to appear to be in straight lines with even spacing and so on. Those are 12x24 inch tiles laid out with 1/3 overlap. The red background is a painted-on waterproof membrane. It's obviously not required for this trial wall, but I wasn't sure how well the thinset would adhere to the unpainted drywall, and the membrane said it would make that all good.

I was happy enough with the result that I made the decision to go ahead with the DIY route. The biggest lesson I learned is that laying tile is a messy, messy business. At last, the earnest accumulation of tools and materials could begin.