Presently I rely mainly on Heists for “maintenance” waves; that is to say, reliable waves of moderate quantity - enough to get 10 levels or so without freaking out about it or spending the whole week grinding them.
Gain access to the Flit; amass adequate Shadowy to engage in heists; we’re talking upper double digits, nothing too overwhelming.
Grow casing how you can through the related storylets; the best source of casing requires a Gang of Hoodlums, the formation of which requires playing a certain Opportunity Card storylet, enduring some decent Shadowy checks and coming up with a LOOOOT of Rostygold.
Either with your Gang of Hoodlums or simply by relying on the storylet which requires PoSI status but NOT a gang of Hoodlums (lesser, but still one of the best), build enough casing to purchase:
-An escape route.
-As many Inside Informations as you care to
Once inside, you’ll need to wait perhaps half an hour for your Heist deck to load. With a couple exceptions, these cards cannot be discarded, so having a higher-tier lodging will actually make you a much better thief. Most cards involve stat, luck or quality checks with loss of cat-like tread as a common punishment, sometimes accompanied by minor Menaces; your most common reward will be a short-term quality called Burglar’s Progress, although contraband and items that contribute to the ongoing heist also come up.
Use Inside Information whenever you can. An option that avoids a luck check is a better one, as is one that has requirements such as a high Shadowy. Don’t engage luck checks until your hand is full and you can’t get rid of any cards without doing a luck check. If a butler finds your escape route, just leave the card alone, even at the expense of your ability to draw cards. Once you have AT LEAST 5 Burglar’s Progress and preferably 7, AND you have drawn the card allowing you to complete the heist, THEN “let him” discover your escape route; you’ll gain another point of Progress (redeemable for 1 MW if you’re on the easier level of difficulty or 2 points on the harder level). From that point forth, playing the card that claims your reward (and ends the heist) IS your escape.
If you get down to one point of cat-like tread, do not engage any more luck checks, even if it means leaving without your reward. Running out can result in insta-jail. At three cat-like tread, there’s nothing wrong with luck checks, primarily those with decent odds and involving humans. Finally, you can absolutely get caught with two points of cat-like tread; some of the luck checks with better odds punish you doubly if you fail; failing a luck check to an animal can be serious business. I wouldn’t entertain luck checks with two cat-like tread until you are experienced with the cards involved and know whether failing on the card is capable of ending your heist
Some luck checks may present you with an opportunity to gain Inside Information or an Intriguing Key; in any case, hope to be able to exchange them for more progress. When the lack of items or a bad sequence of cards finally forces you into luck checks, play them with priority towards maximum chance of success. Some are just plain bad - spiders and dogs are the worst, but cats are actually good news if you have decent Connected: the Duchess.
Finally, cashing out: The best return in echoes per turn, which is potentially very high, depends on entering with minimal preparation and still gaining the necessary Burglar’s Progress with as few turns as possible. Connected:The Duchess, Dreaded, a pair of Intricate Kifers and plain old luck will all assist you; the ideal formula may yet involve one or two shots of Inside Information. You may also want to cash out with 5 progress if able, starting another heist rather than muscling the extra two points - unless you can do so very conveniently.
Waves, however, scale with your Burglar’s Progress. If you amass 20 by bringing in a LOT of Inside Information, drawing a lot of the right cards and renewing your resources by passing certain luck checks, that becomes 40 CPs of MW, which will carry you to MW level 8 from zero CPs. By heisting regularly with proper preparation, you should leave with 10+ Burglar’s Progress and gain 20 CPs of waves reasonably often; and even on a failure, you should get 25 or so Echoes for your trouble by completing a triple-bolted heist.
As has been noted, you should acquire certain items in order to lower the cost of Notability acquisition. Every point of BDR lowers the cost of your next point of Notability by 1, but every point of Notability raises the cost of a further increase by 4. So, in pushing for your eighth point of Notability, you will be at a 28 point handicap (requiring MW 48) before accounting for your BDR reductions. Even with fantastic BDR, you’re looking at a 20+ Waves requirement for that eighth point, even though you can maintain it with 16, which is achievable in 3-4 good heists before accounting for where you’re starting from that week. I recommend Salons for the big blasts of Waves when you’re trying to become more Notable. For where you are now, I would worry less about Notability and Professions for a week or two; maintain 4 MW to keep your existing Notability, and seek out a vehicle, club membership, affiliation and perhaps a decent boat. Your third point of Notability could come as cheaply as 14-20 MWs, which is achievable with Heists if you’re persistent and start early in the week.