I’m not clear about the question.
SMS text messages are sent to phone numbers. So if they are being sent to your landline, then the senders have the wrong number.
iMessage is sent to your Apple ID, and every device logged in with your ID should get the messages.
Or is the problem that your outbound messages are send with a “from” address that is your land-line, causing replies (especially SMS replies) to be sent to the wrong number.
If it’s the third condition, go to Settings → Apps → Messages → Send & Receive. You will see the list of addresses and phone numbers that Messages will receive from, and you can pick the one that will appear as the source of messages that you send. Make sure the “Start New Conversations From” is either an e-mail address associated with your Apple ID or your mobile phone number.
Or, are you talking about sending to someone else’s home phone number? Your Contacts list actually ignores the tags - the “Mobile” tag is just text and doesn’t affect anything.
When sending messages to people with multiple contacts, you will notice, as you start typing, the list of destinations filter down to the one you want. After a few seconds, they addresses will change color from the default gray to blue or green. If it turns blue, then it will go out via iMessage. If it is green, then it will go out as SMS, but the app can’t tell if it’s a mobile number or a land-line.
If the contact has multiple addresses, there will be an arrow on the right-side of the column. Tap it to see them all, including the tags. But it will be up to you to know which of the green addresses can or can not receive SMS.
I think (hope) that iOS will remember your selection, in order to make it the default for future messages to that person, but I think that’s the extent of what it will be able to do.