As usual, soundman says good & writes good.

True-sine inverters are usually about twice the price of stepped-wave.
Ironically modern SMPS PSUs as became popular with PCs & IT equipment and now found in almost all PSUs shouldn't require smooth inputs. (Hey - it was PCs that ruined our smooth domestic AC supplies and ruined the definition of cosΦ (phase angle) as Power Factor, yet they demanded smooth supplies! Hypocrites!)

But being essentially square-wave means infinite harmonics - hence all the noise & problems. And excess heating of some front-end components.
Plus their peak voltage is lower than a sinewave's peak voltage - and SMPS tend to depend on peak voltages. (The input voltage must be higher than the SMPS's internal DC voltage for power transfer Thing if the SMPS as diode that charges a capacitor (followed later by the conversion & regulation crap).)

This whole topic is one full of oft quoted misunderstandings. EG - caps & batteries put "extra strain" on the alternator; dc converters and brushless dc fans do not involve ac; vehicle chassis/bodies are poor conductors, hence bad grounds; etc.
In fact, usually the opposite is true! (As with those last examples.)

Then there is quality & Regulations.
F.ex I read how inverters stateside are rated by PEAK power handling. Not so here - unless clearly stated otherwise, a 300W inverter will handle 300W full time, and it will probably handle 600W intermittently or peak - ie twice as much as its rating until its semiconductors internally overheat. Hence a 300W inverter should be enough to handle a 300W motor - though that could be a bit extreme depending on the start-up current of the motor...

Probably the inverter is best mounted as near the battery as possible. Why? The battery supply must handle more than 10x the current of the output, hence much thicker cables.
However that means AC (120V or 240V) through the vehicle. This could be considered a safety issue - though if "floating" you can touch one side safely; if ground/earth reference (to the vehicle's chassis/body) then an RCD (Safety Switch? offers the same protection as in AC systems - but they will NOT protect you if you touch BOTH AC conductors.
Noise wise - what has more noise - the stuff reflecting out the inverters dc input, or the AC output? True-sine inverters can have disgusting noise on their inputs. Hence why the shorter dc path - closer to the filtering battery, and less length for dc noise to radiate from.

I could go on reminiscing - idiots that wanted ground stakes (ie, 12V inverters "earthed" to a stake in the ground), that fought output earth/ground to chassis and neutral (L2) bonding, "Isolation Transformers" to isolate earths/grounds (thems being a Class of transformer for non-earthed systems - ie, dual-insulated - as opposed to common ordinary "galvanically isolated" transformers to isolate two different earths or grounds).
But I'll try to keep to the stuff that is more likely to cause you pain....

Yet another big-picture ramble, but some get the light.