Rotavating Garden. Advice?

Once the new grass is established and is being regularly mowed briars should not be a problem. Like many other plants the growth in brambles is from the tip so if it is being cut off by the mower it is unable to grow and needs to start producing a completely new shoot, unlike grass where the growth is from the base of the plant. The grass also simply out competes most other growth so you should only need to remove the odd weed if you do a good job of getting it growing right. The roots of brambles are usually not very difficult to dig out once you can get past the thorns to get at them.

Personally I would find just growing grass not very interesting and if you were picking out the stones you could use them to mark out some areas for planting with some trees, shrubs, flowers or even some cooking herbs fruit and vegetables. When I was sorting out my garden there were some areas that were very stony and uneven and would have been very difficult to turn into lawn so these areas were easier to convert to areas for growing other things.