I used to have Les Setilles from O Leflaive as a house white, mainly as Mrs L vastly prefers White Burgundy to the exclusion of almost anything else, but in recent years I have felt the quality has declined whilst the price has risen. I've swapped to their Oncle Vincent cuvee as this is not significantly more expensive yet the quality is still there. I am under no illusions as to how temporary this is likely to be however....
I am constantly on the hunt for 'value' in so far as it exists in Burgundy, so I have been trying quite a few BBs provided the price is right. De Montille's Clos du Chateau is very good, but I have been a bit underwhelmed overall with Ballot-Millot's base white across several vintages. More positively I have recently been pleasantly surprised by Guillemots Gollardes, and Jean Chartron's Eugenie Dupard is very good. I have some Javillier and Marc Colin waiting in the wings, I've enjoyed quite a few of the latter's St Aubin 1ers but have never tried his base wine. I am with Alex here btw, life is too short to drink truly cheap wines - I'd prefer to have one bottle of any of the above than three of something at £8.99 where the value of the liquid element is likely measured in pence.
On red it's not as simple as just having one red, I think you need several. In Chateau L we would almost always have red to accompany food. So for Pinot Noir I've found Rion Bons Batons very good value, and also Pierrick Bouley's BR. Grivots's BR was once upon a time favourite, and Tawse has been excellent for the money too. I once found a case of 2015 for £14 on the table and every bottle was a delight. For Syrah I tend not to stray too far from Ogier's La Rosine, and for Grenache based wines (even though I am going off them) I have always enjoyed the screaming bargains from villages like Gigondas and Vacqueyras provided they have a bit of bottle age on them. We don't have any Cab-Sauv house reds, we eat so little of the food it best accompanies it that when we do we end up going for something a bit grander. I am also developing rather a taste for Langhe Nebbiolo as an alternative to Pinot Noir or to go with Italian dishes. I was blown away last year by Sottimano, and those from Marcarini, Giovanni Rosso and the PdB have always been relatively low-cost options that punch above their weight.
Rosé - these days it's Tempier Tempier Tempier, but in times past there was a great wine whose exact name I cannot remember but came from Leoube. Petit something perhaps, and not in a can! We bought cases and cases of it. Ditto the Duo des Plages from TWS. Last summer was so rubbish that we barely drank any though.