I would invest 10k/week. That gives you 2.5 months. I invested 18k in november/december 2019 and plan to invest 12k this february when I get my bonus. Any more stretching it out is just pure fear of a coming recession. If you aren’t comfortable losing 50% of those 100k, maybe don’t go with 100% stocks.
This thread I started on Bogleheads helped me a lot: https://www.bogleheads.org/forum/viewtopic.php?t=293747
I like how everybody is aware that lump sum is probably better yet everyone seems to favour dollar cost averaging. I am not criticising, I am not in this situation so I don’t know what I would do. Funny how human psychology works.
The biggest psychological hurdle at your stage is not to invest and wait for the big dip or crash. So by starting with little money you are in the long-term game. And you will sleep well. Don’t forget, with 25 of age time is your best friend. What ever you decide you will have a smile in 20 years when you think back and reflect about those many thoughts you had today.
Slightly off topic, but a book that helped me make sense of natural tendencies towards “irrationality” with respect to money and investing (such as doing DCA instead of a lump sum) was “Thinking Fast and Slow” by Daniel Kahneman (he’s a psychologist/behavioural economist who has been mentioned elsewhere on this forum… FI, happiness, mid-life crisis & depression - #29 by 1000000CHF ). Tons of relevant material, but the sections on risk pricing, marginal utility, and differences in responses to gains and losses were super interesting.
Which is not entirely unjustified given the current environment, is it? 
To sell, not to sell, to buy, or not to buy? That’s the question…
If you google “stock market to gdp ratio” you get interesting charts like this:
Market timing doesn’t work, so the answer is obvious.
Stock market returns aren’t really related to GDP growth. Especially with a market like the US where almost half of the revenues are made abroad.
There is no question here- this question was answered in all statistical models.
You know what the math says- buy and hold without trying to time gives the best returns. You think you can beat the statistics feel free to go ahead and try to sell. Why not?
You can also win a million dollar from a lottery, the statistics says you will not - but every month some individuals do win. Maybe this time it’s you?
Well, it is not only a question of buy or sell, there are plenty of possibilities between (depending on “how much”). Like just “hold” (or HODL 
), in the middle.
But market valuing does (look at p/e, yields, etc.).
You can adjust your expected return based on valuations, but the expected return at high valuation is still better than cash.
It would be cool to determine a function of CAPE (for instance) that adjusts the buying intensity. Finding the optimal function in terms of profitability over n years of CAPE historical data could be a nice problem.
what is buying intensity?
CAPE generally increased over the last 100 years. It’s pretty useless for market timing.
Say you have 1.0 cash unit to invest each month, 0.0 would be “do nothing”, 1.0, “buy buy buy”, 0.5 would be “invest half of the sum” etc.
You could de-trend it.
I think the only good way of using CAPE might be for the SWR once retired, for example 1/CAPE = withdrawal rate.
1.0 is always the best option.
You can use CAPE to adjust your expected return and make your financial plans based on that, but there isn’t a way to use that information to improve your risk adjusted returns.
