Tips for an easier transition to a new tenant

[Mike S.]

• Hello everyone -
  
  I'm still a newbie to being a landlord (first time transitioning from old tenant to new) so I'm hoping some experienced people can help with how to transition from old tenant -> vacancy -> new tenant quickly without cutting corners on vetting.
  
  Situation:
     - Recently renovated 2 Br, 1 Ba, ~1100 sq. ft. basement unit of up-down duplex just south of Denver. I inhabit the top unit.
     - Tenant was excellent and will be in the property through the end of March (Started 1/20) - having her draft up a written notice saying she's leaving. Have a good relationship with her (would definitely be a reference) but moving out because she wants a place of her own.
     - Don't anticipate many, if any, repairs other than nail hole and minor paint touch-ups
     - Written into the lease that I can have prospective tenants visit while she's still there (with notice)
     - There is room to increase rent by at least a couple hundred dollars/month (I made several improvements in the time that she's been
       there) and it will still be reasonable
     - She said she has a friend that may be interested in renting it

• Primary Questions:
     - The most interesting thing to me, at this point, is the friend - she is familiar with the property and may be able to move-in quicker than someone new (Disclaimer: I have not spoken to her yet, just spitballing). However, she obviously will know the old rent price, making it harder for me to raise the prices to what I think I could get. If she passes background, etc., is it worth a smaller raise to limit vacancy and go with a better known commodity?
  
    - What type of person/people should I look for that might stay in the property a bit longer term? It's in a great location - walking distance to grocery store, great bars/restaurants, concert venue and a light rail station that can take someone into Denver, etc.
  
     - Showings: How do you typically handle the balance of showing the current tenant's space to a new prospect? She's neat, but is it weird that it's filled with someone else's stuff when they're looking at it? How do you talk with the new prospect about it?
  
     - How have you handled the transition, timing-wise, from old tenant to new? With her leaving on March 31, it's not like I can just put someone in there on April 1st without doing the minor fixes, cleaning the place, etc. Right?
  
     - What are other logistics I need to know about that I haven't mentioned (i.e. move-in, move-out checklist timing, etc.)?
  
  I really appreciate everyone's thoughts and, if you've seen a good post of this topic before, I'd love the link to it as well.
  
  Thanks!