I have never used a private car service in Italy, at least none that I can remember, as I always drive my own rental car or some family member's car, therefore I can't recommend any in particular. There are however hundreds of such companies in Lombardy and I'm sure they are all reliable. Just to check prices, I checked with a major one based in Peschiera Del Garda called www.PeschieraTransfer.it.
For four pax with 1 suitcase each they charge about €300 one way. They offer a 20% discount if you book and buy a round trip transfer.
These are the alternatives:
1. Rent a car at MXP and drive your own car. €300 is about the price of a midsize car per week. That way you will have your own transportation during your stay. I know Garda well and frankly I think a car is useful in that area as trains serve only the south lake.
2. Go by train to Desenzano, then a taxi to your town.
The Malpensa Express train takes you to Milan Centrale in 45 min for €12 p.p.
Then from Milano C. there are two trains every hour to Desenzano. The regional trains take 1h25m and cost about €9 per person one way. The faster (but only 25 min faster) Frecciabianca trains take you there for €20 per person.
So basically the train option would allow you to get to Desenzano for a price ranging from €80 to €120 for the four of you, that is about 1/3 of the price of a private car transfer. Time wise the train is likely even faster than the car if you take a Frecciabianca, in spite of the layover at the Milano Centrale station.
I gave you the options. You think it over with the rest of your party. I would rent a car, but that is me.