Generally, my impression is UA miles is better for Europe and MR points have better transfer partners to Asia. However, UA will get you to Asia and MRs will get you Asia. So both are great programs to build points and miles in.
As for which card(s) next, it kind of depends on the offers you can get.
If you can get targeted for the Amex Platinum with a 100k MR points offer, that's just one slot.
Have you tried to see if the Amex Platinum pulls up on Cardmatch with the 100k MR offer? See
https://www.doctorofcredit.com/cardmatch-offering-people-100000-points-american-express-platinum/
Are you looking at both the United Club card and the Explorer card? That's 2 Chase slots you'd be using up for between 90k-110k UA miles.
The Club card gets you priority boarding, first and second checked bags free (must pay for tickets with card), United Club membership, expanded award availability, and a 50k UA miles signup bonus, but its $450 AF is steep, so you'll need to evaluate whether Club access and free checked bags (but only on tickets paid for with the card) give you enough monetary value to justify the cost, or if you're signing up for this card primarily for the miles. Earlier this year, United was sending out targeted offers for the Club card that waived the first year AF. My wife who flies United frequently for work, but doesn't already have a United card, received the targeted offer. (We passed.)
The Explorer (new MPE) card gets you priority boarding, free carry-on for basic economy, first checked bag free (must pay for tickets with card), 2 United Club lounge passes, up to $100 credit for Global Entry or TSA Precheck, a 25% mileage bonus on United’s MPX gift card app, and probably most importantly, increased award space availability. You get access to additional award seats that United blocks off for their cardholders and elite members. The $95 AF is waived for the first year. Chase has no fee United cards you can product change to after your first year that’ll still give you increased award availability.
But wait until you can get a good signup bonus on the MPE. Chase is known to deny matching to better offers on United cards.
The current public offer on the MPE is only 40k UA miles + $100 statement credit after you spend $2k/3 months. For much of last year, the public offer was 50k UA miles, with a targeted offer of 70k UA miles. There's buzz that there are better 50k and 60k UA miles offers out there (
https://www.reddit.com/r/churning/comments/8q8d13/daily_discussion_thread_june_11_2018/), but these are likely targeted and you'll have to log into your UA account to see if you qualify.
If you don't see a targeted higher offer, don’t settle for the public 40k UA miles offer just yet; there are some tricks that have worked to get you targeted for higher offers on the MPE:
- Fly on United. After you’ve flown on United, many people report getting targeted with higher than public signup offers for the MPE (and Club card) via mailers and on their United account in the following weeks.
- Make a dummy booking on United. Log into your United account and go through the motions of making a flight booking, and you may see a popup offer for the MPE with a higher mileage offer (and possibly statement credit).
- Make a purchase through the United MileagePlus Shopping portal. People have generally received a targeted mailer a few weeks after their portal purchase. The MileagePlus Shopping portal includes iTunes, so you could possibly trigger a higher credit card offer by buying a cheap song.
- Make a purchase on the United MileagePlus X (“MPX”) gift card app. The MPX app is available for iOS and Android devices and sells e-gift cards at face value, often in the exact amount you need, but allows you to earn 0.5-5x UA miles/$1 depending on merchant (more during promos) and passes the coding of the purchase on to the merchant’s category allowing you to trigger category bonuses on your Chase Visa credit cards.
These tricks may trigger a higher offer immediately or could take several weeks to work, if at all. Since you're looking to apply as soon as a month from now, you should probably start with the above. Keep playing around with the above tricks, as there seems to have been a lot of success with them last year. It probably helps if you don’t already have a United credit card.
Good luck!
. Will probably be spending quite a bit at restaurants/on food during our CA trip at the end of the month (returning 6/30), no 5x category on either CF or Discover. Will probably be using Lyft a decent amount while there, but Q3 doesn't start til after we leave lol. 
How did that happen?
Anywho… His offer was 50,000 miles plus $100 credit. Is that one worth going for or should I wait for a better offer? 70,000 sounds better. My plan is Europe sometime in the next few years, but I have nothing specific planned. My DH is 2/24 and besides somehow getting the Southwest CP pass in January we have no other CC plans for him. Was hoping to get something soon to spread it out with the SW apps in December/January time.
I've gotten the feeling that this group is welcoming to all types 
