The optimal time to start would be during an event, such as 59M Downloads to get the extra 20 Catfood as a daily reward when beating Japan. Other rewards, such as a Free Rare Ticket on Meow Meow Day are more preferable. To know when these rewards are available, look at SilumanTomcat's community page. Other things to look for are Sales. The best Sale would be the Half-Off Item Sale, letting you save upwards of 50 Catfood from buying Speed-Ups, which quite literally half your time. If that's not on, the Special Cat Discount is nice to, saving 25 Catfood for Ninja Cat. If neither of those are on, I'd advise against starting unless something else is occuring. You also need to pay attention to sets. Ultra Souls is the best one, then Pixies, then the Fests, then the rest of the sets in no particular order followed by the Nekolugas and Dragons in last. The chances of getting a good Uber in any of the sets between Fests and Nekolugas are pretty rare, so I'd advise against them if you're going competitively. For a very un-official, but hopefully accurate Tier-List of Ubers to use and who to sell for XP is here (https://imgur.com/68t4PYt). It prioritizes Cost, then Abilities such as Wave, then Cooldown, followed by the helpfulness in THE MOON, since it can sometimes take about 5 minutes to beat without good cats.
When starting, you want to level up Cat as much as you can to cruise through the earlier stages, but save 5,000 XP for unlocking Gross Cat. In Japan, when using one of the Free Rich Cats, you need to stall the beginning peons and Those Guys with one or two Wall Cats while stacking 2-3 Gross Cats for when you hit the base. Wall Cat is normally enough to ensure none of the Gross Cats die, however, they may get KBed. After you beat Japan, it's important to do a few things: Get the Gold-Officers pass, getting 1 free Draw and 30 Catfood. Use the single Silver Cat Ticket, getting the Mission which gives 20 Catfood. Buy enough Speed-ups to Reach the Moon. Then, you can go on to the Rare Gacha. A few cats, such as Salon and Rocker are very good, but the majority you'll trade for XP. The only Super Rares worth keeping are Hip-Hop, Swimmer, and Cutter Cat - the Rest can be traded for XP to level up everything to 10 (Keep in mind you cannot de-evolve until beating EoC1, so do not level up Ultra-Souls or Uberfest Exclusives to 10.) Go to the Cat Guide and claim the Catfood if you're close to 200. If not, don't bother and just buy Ninja Cat and level him up to 10 as well. If possible, get the User Rank reward for 100, getting 1 Free Rare Ticket. You'll want to save XP for Cow Cat, but level up Wallet, Research, Energy, and Worker to 10. From there, it's all luck from Gacha. If you're lucky, keep the run. If you're barely getting enough XP to level up a single cat, restart. Once you get to the MOON, make sure you've saved another Rich Cat. Most Anti-Floatings will be helpful here, and this can sometimes prolong the run for 5 minutes, so putting the time into creating a New Lineup could be helpful.
Other Notes: Favor Ninja over Giraffe if low on cash. Just because it's an Uber doesn't mean it's good. Super Rares are another name for XP. Using the extra Rich-Cats can shave off 15 seconds, so using them in the correct stages could help.