Doing solar PV and the roof at same time is definitely going to be cheaper just cause you can share scaffolding etc. Solar PV as the roof is probably much more expensive.
Those tesla solar tiles (or similar) have lower yields per m^2 and therefore cost far more than a mass produced standard module per kW (usually the increased area and efficiency doesnt even compensate for losses due to tiling using standard modules due). I think I even read somewhere they have efficiency of ~5%? This is compared to 18 - 20 % for a standard module. So you would need 4 times the area covered than using standard panels. Losses due to tiling wont exceed 20% so standard are generally much better. They only make sense in some parts of US I think with big single storey houses with massive roofs. In Europe with limited roof areas they are a waste of money.
For other integrated mounting systems , some require bespoke modules which , like solar tiles, is probably going to be quite pricey per kW. There are some systems which use trays which are compatible with wide range of standard modules. If you want the integrated ‘look’ thats probably the best compromise as these wont be much more expensive than racks (but you might be charged more for fitting).
Otherwise i would just procure the two separately and do at same time. Obviously can cross-check with both contractors to make sure they arent doing something which makes the others life harder etc.
My main advice: cram as many standard modules onto your roof as you can. You are not actually restricted to 3.6kW in terms of module output, that is the limit for the inverter output on single phase connection. The marginal cost of fitting more panels is tiny compared to all the other costs now. Inverters are now designed to be undersized wrt PV output for this reason. For example, the new sunny boy 3.6kW can take up to 5.5kW in terms of peak panel capacity. It just clips panel output if it exceeds 3.6kW, but it means you get more output over day and either side of summer peak. This will boost your yield for little extra cost. There is a lack of awareness of this even amongst installers.