Bearing in mind that it was often a bit mixed up depending who was present at a particular battle and all the social and political niceties..
Captain General- Head of the armed forces, Generalissimo – eg Cromwell (not sure if Charles I was counted one?) more of a title than a command
Lord General – commander of the army – eg Lord Forth, later Rupert; Essex, later Tom Fairfax (NMA)
General – sometimes used as short version of above or for commander of a smaller army
Lieutenant General of Horse – commander of the cavalry eg Rupert at Edgehill, Cromwell at Naseby and Marston Moor, usually led the right wing
Lieutenant General of Ordnance – commander of the artillery, not usually leading troops around in battle eg Hammond in the NMA
Sergeant Major General- commander of the foot eg Sir Jacob Astley, Philip Skippon – usually led the centre
Major General – short version of above, or commander of a regional force eg Cromwell's Major Generals
Commissary General – second in command of the horse, usually leading the left wing eg Wilmot at Edgehill, Ireton at Naseby
Colonel-General – not really a battlefield post afaik, usually the senior commander in a county or region. Could be used for overall command of a lesser arm eg Sir Arthur Aston was Colonel-General of the royalist dragoons.
Brigadier – not really a contemporary rank afaik, but certainly a contemporary position. Brigades were usually either of horse or foot, but could be mixed. Usually they were led by the senior or most active Colonel. eg Bard, Sir Bernard Astley and Lisle at Naseby.
Also bear in mind that often an army was comprised of troops from various different commands eg Leven, Fairfax, Manchester, Newcastle and Rupert at Marston Moor, so each had their own hierarchy of generals.
by the way, here's the list of staff for the New Model Army link which goes into the detail of other staff.