Let me pose this to you -- why do you think your prayer life is improving with the use of a prayer rope? Why has having the right "equipment" as opposed to praying without helped you? After all, the Jesus Prayer can certainly be said without it, or counted on the fingertips if you're really concerned with keeping count.
(Don't read any Internet aggression into these questions. Just trying to provoke some reflection and perhaps help you find an answer.)
That said, if using a prayer rope is helping you improve your prayer life in a real and meaningful way, then you probably are on the right track.
No offense taken and thank you for asking these questions because I think they're important. In answering these questions I believe that maybe on the right track. To answer your questions I would say this: What I've noticed is that the prayer rope is a visual reminder to pray so when things in my day distract me I'm immediately reminded. After reflecting on this, I guess what bothers me or causes me to question myself is this. I have good prayer time when I'm alone but when I'm at work I get distracted and forget. I saw an interview with a monk who said he prayers constantly, even when he's in a conversation. After I heard that I felt like my prayer life was seriously lacking.
First things first: don't beat yourself up over the fact that you don't have the prayer life of someone whose life is dedicated to prayer. Your information says you're a catechumen, so it's just not likely you're going to be able to pray like a Schemamonk. Crawl before you walk and all that. I'm not saying you shouldn't have goals, I'm just saying that there's a difference between short-term and long-term goals.
If a visual reminder is what you need during daylight hours, find something that you have around you during the day (something on your desk, whatever) and mentally flag it as the thing that will remind you to pray.
Remember, Orthodox prayer is not about our personal accruement of liturgical or paraliturgical items, it's about repentance.