Backsplash for behind stove
There is no requirement for a back splash behind an oven.   Period.  I buy a lot of houses with just drywall and painted.   

To add tile there is very little prep work that you have to do to the wall.   Basically you just want to scruff it up a little if tiling with mortar and if using the peel and stick, a rough sanding and cleaning up after works.   

Whether you choose the peel and stick or mortar backed tile, that is just a personal preference.   I would suggest either way to get something that is durable, cleanable (without ruining the tile), and something that won't stain.   

My go-tos for backsplashes are glass tiles or small natural stone pattern (with no grout requirement).   For the glass backsplashes I only use epoxy grout.   Epoxy grouts are a PITA to deal with but for backsplash areas they "pop" and they are almost impossible to stain and require zero maintenance so I deal with it.

As for how hard of a job this is I will give you working example.   

Lets assume a 3'x 8' area needs to be tiled.

Using glass tile + epoxy:


Take about 15 mins to prep.
15 mins to mix a small amount of mortar.
If you have a helper, mortar is only applied to wall.   So one person can apply mortar and the other adjust tile sheets.   
Given there are cabinets a wall you should only have to make cuts to one vertical line and one horizontal line.   And really on 90% of installs I do very little cuts.  Score and snap glass.
Even for a first timer putting this amount of tile up is no more than 2 hours.   If it takes longer your mortar will dry anway.   I have people on my team that would be done with this in 30-40 mins.
Come back next day and apply epoxy grout.   
Now this is a two person job because the grout will set in about 30-40 mins.   You need one person applying the grout and a person going right behind cleaning up.  The good news is even though a total PITA - you are done in about 30 mins.


With smaller stones:


Same prep
Apply mortar to wall and a very thin amount to the back of the tiles (read instructions).   
Will need a saw to make cuts - still should be able to work out pattern to limit needing to make cuts.   Sometimes we break apart the sheets and try to find stones of a size to meet needs.    
The cuts take longer and the back buttering of the sheets takes longer and adjusting these to line up take longer than glass.  But you are going pretty slow if at 3 hours.   
You are done - some stone might require a sealant to protect from staining but that is 5-10 mins of wiping the face of the stone.


Note: I specifically would never install porcelain or ceramic tiling (unless some super cool-artsy mosaic) because I never want to worry about it.   You are lifting pots and things like that.  You hit these hard against the tile, they can and do crack.   Glass will not crack.   Small stones, you just replace.   (I am old school so not even considering peel and stick as the amount of shopping and research behind a brand would negate how fast of an install this is)

Disclaimer:  This was not meant to answer how to tile or how to apply epoxy grout or the exacts.   Please ask a separate question for each of these topics to be answered.